love the way professor Adams explains things, i'm starting to get my master degree in physics and yet by watching these lectures i feel the need to study more,it's like MIT courses makes you realize you need to learn more and more and more... and it's never enough!!!thank you MIT opencourseWare for giving me the opportunity to experience quality courses with these great guys. love you
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Although they are smart, they may not be as smart as you think. Most of these guys studied QM either on their own (e.g. reading books like QM for Dummies or watching RUclips etc) or took QM course before arriving at MIT. Yes indeed, there are schools that give introduction to QM in High School. So, if they have done that, they are pretty smart. But realize this may not be the first time they are seeing this. So, smart indeed. But maybe not quite as smart as you might want to believe.
As this is on OCW you have open access to the lectures, recitations, and problem sets as well. If you really want to learn quantum mechanics I highly suggest you look into this wealth of information.
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explain the point of all this. What is it trying to achieve, why and how? Try to explain what all these equations are telling about time and how time works. Without complicated words.
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@@Saptarshi.Sarkar Yes we totally get that but what he means i guess and i agree with him on that, is the fact that so many questions asked in that class improved my understanding of the concepts, like every question was necessary, without those students this class wouldn't have been the same and the prof was brilliant at understanding the questions as well as elaborating and answering them. It's like everyone in that class played a role in teaching.
As a holder of a computer science degree and another in electronics I bow to the recognition of reality. Circuits and code only do what they are made to do as does your world. So cool. Thanks for the pump.
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Really good explanation - excellent lecturer (Allan Adams); he actually invites questions, repeats them and then gives cogent answers. It's the first time I've seen someone explain the relationship between eigenstates and Schrodinger's equation. Also how superposition falls out and is effectively a consequence of 'stationary states', therefore unaffected by time. This creates a physical distinction between the quantum world and the classical world, as he explicitly demonstrates; the interface being the 'collapse' of the wave function or 'decoherence' as he calls it, when superposition disappears. Since the wave function is 'all you need' and SE is 'not derived, just posited' makes me think it's a good candidate for the 'God' equation, meaning it fundamentally describes everything that's yet to come into being.
These really are great lectures. I'm using them to supplement my coursework and they're really helpful in giving meaning to the equations and solutions i derive in my homework. For instance, I have a midterm tomorrow and i feel pretty good with my ability to handle the math and solve problems; but if asked what my solutions imply i would be hard pressed to answer without the intuition i gain from these vids. This lecture series really helps build my understanding of the material. Thanks MIT OpenCourseWare!
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explain the point of all this. What is it trying to achieve, why and how? Try to explain what all these equations are telling about time and how time works. Without complicated words.
Stellar professor, excellent lecture. I have studied physics myself and got really frustrated. I know everything there is to know about boring physics lectures. This one is motivating, interesting and entertaining. Big up for Professor Adams.
Concerning the discussion of infinite combinations of continuous functions becoming discontinuous at 24:38 I would just add that while it seems merely theoretical it provides further evidence of quanta. We have must have exactly so many wave functions interacting or we can break things like smoothness and continuity which match closely with observation. Limiting behavior defying observation is also what led to the ultraviolet catastrophe, another artifact of quantization.
For those already initiated in QM I repeat here some comments previously made to similar videos. They may clarify debatable points. The Schrödinger time dependent equation (STDE) when applied to a wave representing an initial state of, say, an electron bound to a proton and together forming a hydrogen atom, predicts and retrodicts all the future and previous states of the electron wave, in the same fashion than the evolution equations of classical mechanics predicts the movement of the Earth around the Sun. Note that the STDE is energy conservative, that is, the initial state as well as the predicted and retrodicted ones all have the same energy. As is well known the bound electron has a completely different conduct. Whatever the initial state and in absence of other interactions an excited electron will settle in a stationary state radiating energy (in the form of a photon) along the way. If the stationary state is the ground state the electron will stay there forever (in absence, as said before, of other interactions). Otherwise the stationary electron state is ephemeral and will be abandoned to radiate a photon and assume a new stationary state of even lower energy. This "down the staircase" process repeats until the ground state is reached. There is no manner to adapt the STDE to this physical process. This inconsistency was discovered by none other than Niels Bohr, as can be inferred from the report of Werner Heisenberg. See our note www.researchgate.net/publication/356193279_Deconstruction_of_Quantum_Wave_Mechanics After discovering the tremendous inconsistency it would have been natural to announce that the STDE contradicted with physical facts, and ask for a correct equation. I assume as true, but only know from hearsay very long ago, that in Einstein's viewpoint the correct deterministic time dependent wave equation had to be non-linear. References to this historical detail would be appreciated. It is hard to believe but, against reasonableness and common sense, Bohr decided to adopt the STDE as correct and that continuity, causality and determinism of physical processes were wrong because they contradicted the STDE. Apparently mathematical equations on paper were more relevant than the experience of the whole human race. Then a series of new and fanciful "quantum physical principles" were adopted. In my opinion the powerful quantum establishment dogmatically defends Quantism and strongly rejects any attempt to correct its misdeeds, even if the correct deterministic time dependent wave equation available. With best regards to all. Daniel Crespin
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explain the point of all this. What is it trying to achieve, why and how? Try to explain what all these equations are telling about time and how time works. Without complicated words.
22:00 So, why are the superposition principle and linearity different from each other? How can you have a linear wave equation without your wavefunctions obeying the superposition principle? How can the wavefunctions obey the superposition principle without the equation of which they are solutions being linear? Are we making a pedantic distinction between physical properties of a system and the mathematical properties of the equation that describes that system?
tokamak An example of a nonlinear equation that has the superposition principle in it: sin x = 0 It is nonlinear (as you can readly tell) and its solutions are integer multiples of pi (neatly already homogenous) when considering just the real numbers. If you sum two solutions (equal or different) you get... Another solution. And that is additivity or superposition, at least in a very simple way. If y and z are two of the solutions of the equation above, one can clearly see that: sin (y+z) = sin(y) cos(z) + sin(z) cos(y) Because always when sin(x) = 0 => cos(x) = 1, implying, for instance: sin²(x) + cos²(x) = 1. Then: sin (y+z) = sin(y) cos(z) + sin(z) cos(y) = sin(y)*1 + sin(z)*1 = sin(y)+sin(z) = 0+0 = 0 As you can see superposition DOESN'T imply linearity. But the converse is true - even if there is no proof here, there is plenty of it elsewhere. Notice, however that this property doesn't apply to all x in our example (just the solutions, which seems to be good enough) and that it is not homogenous for all x in our example for similar arguments, even if homogenous for all solutions - and that seems, again, to be good enough. So superposition and linearity are different properties from each other, even if they are somehow related to each other. You can't have a linear equation without the superposition principle, but you can have a nonlinear equation WITH the superposition principle. We are not making a distinction between the properties of a system and the mathematical properties of the equation (but that is not physics or math, it is philosophy: some scientists would say you should make such distinction - Bohr would say that, actually - and other wouldn't); they are different properties. But your third question, I think, is not answered. What nonlinear wave equations with superpostions as its solutions can exist? I don't think we really KNOW the answer to this question. I've seen some examples of nonlinear equations with a superposition rule or a superposition principle even. But I don't know of any equation like that in quantum mechanics (I'm not an expert in nonlinear equations, though, and I think one could readly say that as well). So it would be interesting if somebody could tell me about some examples concernig such topics, just for curiosity - what I readly checked, in a quick search, was not entirely satisfactory or conclusive for me in that matter.
to use a schrodinger equation first the superposition disappears and the wavw function collapses to a single one. so because the wave collapses i believe it needs not support the superposition principle.
+Tom Franse The prerequisite math listed in the syllabus is 18.03 Differential Equations (or 18.034 Honors Differential Equations). You can find the MIT OpenCourseWare version of 18.03 at: ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011
+Tom Franse It's amazing how much easier this material becomes once you've had linear algebra and differential equations. I watched some over one summer and was just floored at how "hard" the subject was. Took those math courses now it's no problem at all.
For anyone who would like introductory visual representation of the linear algebra, this link is from Yale's BioChem-101 lecture introducing the Schrodinger equation: ruclips.net/video/B4VSqAB_JcU/видео.html
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then! He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
You can also get some idea of the "decoherence" problem by determining the TYPE of infinity that the solutions can fall into when this occurs. Is it the smallest COUNTABLE infinity (Aleph Null in Cantor's system) -- the "rational numbers" -- or some higher infinity, such as the number of points on a line, "C" (called this because there is no proof that it is the next-highest type of infinity, though to my knowledge there is nothing between Aleph Null and C), which is, I think, the 'real numbers"? The former has separate, discrete values and the latter does not (its members flow smoothly into one-another with no "edges"). It seems to me that the former has to be true since all observers looking at a given result in a given universe see the same result, while the latter would allow somebody somewhere in that same universe to see a different result (slightly different or perhaps even very different), since the are no rigid "edges" (gaps between) to the values observed.
A genius can be defined as someone who can redefine the obvious in such a way so as to return something of value that is beyond those who do not understand on this said genius level. This guy nails and proves it. People at work are getting tired of me telling that everything reduces to waves, probability statistics and magic, pure “fing magic”. Not a student but I love this stuff. Don’t stop.
52:30 Ok, what gives here? Stationary position for a particle. As soon s I measure position, I know the positin exactly. Therefore momentum is completely undetermined. Therefore it's almost certainly going to move - the probability that's momentum is zero, which it must be for it to remain stationary, is nil. So how can a particle ever sit still *when we know where it is*?
To be honest, this is such an amazing lecture like we too learn quantum mechanics in class but it seems like those students that are asking questions know more than my teacher.
explain the point of all this. What is it trying to achieve, why and how? Try to explain what all these equations are telling about time and how time works. Without complicated words.
Hmm I am not that good in quantum mechanics that I should fully understand the whole lecture, but how much I got it's that here he tells about when a system evolves it means with respect to time, for that we use shrodinger equation while it is rich in concepts like you just can't precisely measure two non-commuting quantities , it gives that probabilities but not an exact number. When he talks about the eigen value , where he tells about superposition of states ,and so many more
@@pompookgantsu2286 Time is that which the clocks show. We tried to explain that to you when you were five or six years old and then again when you were in high school.
I've some questions regarding this lecture. 1. If the momentum is variable in nature during travelling of any object, then what could be the predictable approximation of Schrodinger wave function ? 2. If the time gets collapsed or the time starts to run backward, I mean reverse, then how the wave function can be expressed ? 3. As severally we read the time gets stopped inside the black hole, then can we really call a particle existing inside the black hole, as in eigen state ? ** If not so can it be possible to apply the time variant wave function at that place for computing energy ? *** If really we can't apply the time variant wave function, then is it true that the wave nature of any object disappears inside the black hole ?
I know you're long past this question but this answer is for anyone else with the same question. What if the function is e^t? The time derivative of e^t is e^t, right? So the time derivative at t=0 is 1. That is, if Psi(t)=e^t then Psi'(0)=1. We have to look at what the function is. Usually the time-dependent part of the schodinger equation is given by something like Psi(t)=e^(-iEt/h) so we would NOT get 0 if we took the time-derivative at t=0. Now, what if Psi(t)=e^(-kt)? Then Psi'(0)=-k. Etc. etc.. etc..
We discussed that we can-with superposition of Eigen state Schrodinger equation solutions make approximately solution to the Schrodinger equation for any state, where the coefficients are the norm squared of the probabilities. Does it make sense in any way to map those coefficients into something like a maclaurin series-so like for each value of the nth derivative (n is an integer) of the function you get a coefficient, with everything else equaling to zero? - to account for the collapsing. But the problem with that would be we won't know which coefficient corresponds to which collapsing. So maybe we could take combination (product) of all such derivatives in all terms-but each degree of derivative evaluated at a different value than every other in a term and than the same variable in every term-in such a way that the symmetry takes away every term other than the one or two that we are able to compute. The combination of all possible degrees of differential functions would mean-okay take everything else as constant and how does this change-remove thay-now everything else as constant and how does this change and so on. While the equation itself would be very long to write down unless someone finds a clever approximate non-polynomial function -but we can still clearly be able to identify the terms that don't cancel out. Is this the formulation of Max Born interpretation-so that the series continues to exist even after measurement.
At 48:10 the ability to convert between energy and momentum is situational, is it not? That is, not all energy would be equivalent to momentum but we can do so in this problem due to the location of the particle being the aspect of the state we are evolving over time?
@@schmetterling4477 Thank you for your reply. That confirms I’m misunderstanding what the nuclear engineering lectures on here are saying about energy transfer being affected by the momentum of the particles in question
Newton's equation F=ma is not "just posited." You can derive it using an action principle involving the Lagrangian. Where is the corresponding process for Schrödinger's equation?
45:36 that equation is nothing more than f'(0)=c where c is a constant. It is just a initial condition. How could he get the following equation at 46:00?
46:00 Here I think he used his conclusion (what this tells me is that under time evolution, a state which is initially in an energy eigenstate remains in an energy eigenstate with the same energy 46:51 ). He did not prove this conclusion. He used his conclusion as his assumption in the process to obtain this conclusion.
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then! He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
I took QM as an elective course in my electric engineering program. I can guarantee that if you had a solid core courses in calculus, diff eq, vectorial calculus and stochastic methods you will succeed and be just fine. I can define QM as a probabilistic method of understanding classical physics and in my opinion is what really happens in our everyday world. Good luck to the ones that are completing the course today. If I can help just let me know. Regards and good luck
This depends on the state you are measuring. If you measure a quantity for which you are in an eigenstate of the corresponding operator, then yes, you are 100% sure that the measurement will give you the corresponding eigenvalue. However, you can also have a state made of multiple eigenstates of the observable you are trying to measure. In that case, all you can say is what is the probability of getting a particular eigenvalue, which is given by the absolute value squared of the corresponding expansion coefficient.
At around 14:07 Dr. Adams says, "The time derivative of position is the gradient of the force." What does he mean by this? Did he misspeak here? First of all, forces are vector quantities, so you can't take gradients of force functions (only divergences or curls). Second, even if you took, say, a one-dimensional ordinary derivative for Force=F(x), how would that give you velocity? I'm confused...
50:45 why did he say that probability is whole function squared, when Postulate no 3. says it is only coefficient (in this particulare case exponential function) that should be squared to get the probability?
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then! He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
I love how the professor's level of passion for the field grows as the class progresses; clearly amped by the class grasping these counterintuitive and gorgeous mathematical models. It makes me nostalgic for those few short years of intense study, when you could pay to learn what you wanted to learn, in such a focused professional way; several radical departures from the first 12 years.
something like would have to work out constants but using a seperation of variables with 3 functions, 2 of t, 1 of x? but i started learning PDE last week and havent spent 24 hours since first lecture here... f ~ exp{(a + bx**2t)}
And so I base my argument to hold my thesis that time is equal to movement times distance and from here forward understand when I look upon a thing in physics thus be applied.
I have a good question,first there was an experiment done where they watch atoms and in the experiment not sure but they could observes the result of atoms traveling trought light and they where all messy but when observes they where all " calm " witch does work with schrodinger the atoms are messy and calm at the same time BUT my question is get the experiment going watch it and observe , it will be calm after that some how time travel and with the same experiment in theory the result should be the same but if you don't observe it will those atoms will be calm or messy ? is ( easier explanation is would time travel affect the same experiment?)
Thank you for sharing these videos ! I have studied the first one and I enjoyed them a lot !! I love the way Quantum Mechanics is teached and the very positive atmosphere of these lectures. I have found one explanation that didn't convice me. This is at 46 min about, during the solving of Shrödinger Equation (SE). Indeed, SE is simplified by replacing Psi(X,t) by Psi(X,0) and by replacing Energy operator by Energy Eigenstate. This is strange to replace Psi(X,t) by Psi(X,0) under the time derivative symbol because the result would be 0 in that case ... I think that one could apply Shrödinger equation at time 0 instead and therefore replace Energy operator by Energy eigenvalue and find the solution around time 0, then resolve this equation at time Delta t and so on ... and conclude that general solution is the one that is given in this video (perhaps another more straightforward way is possible). P.S.: sorry for my english, I am french ... nobody is perfect :)
Let's say at an instant we express a wavefunction as a superposition of energy Eigen functions. How can we prove that the time evolution of the wavefunction is given by the sum of the time evolutions of the individual Eigen functions. He said we can do it, but how can we prove it. I mean what if a particular superposition is only valid of an instant. I was solving the Schrodinger equation to prove this, but I am stuck
Can someone explaint to me why in the last exemple k*L = pi(n+1) and not pi*n, L is positiv but why k couldn't be 0 since it is at the boundary and outside the box?
Time as we perceive it seems like a side effect of our use of numbers.there are periods of time.if we evolved without numbers? Like a smart bird, would we be intelligent? Would we wonder of time?
what, if anything, is the effect of electron mass of the time evolution? presumably the electron cannot travel faster than the speed of light, so does the mass set conditions on how much space an electron can travel in time given a certain energy value?
malaise69 In quantum mechanics the electron mass is always the rest mass, at high energies you should take into account relativistic effects then change the theory to relativistic quantum mechanics or even more to quantum field theory then the electron now becomes a field and the mass is only a parameter of the theory.
So, half way I say time is adjustable through observation. Matches the philosophy that we create what do observe. I’ll be back to edit. Decoherence is an optical term.
I think 46:00 is WRONG. First, he needs to assume that the E-hat operator doesn't concern t, in order to get the bottom-left equation. Second, the bottom-left equation is evaluated at time 0, he shouldn't just extend it to any time t without a proper argument, and obtain the bottom-right equation. I don't think I can trust the lecture series any more.
The operator he calls "Ehat" is actually "Hhat", the Hamiltonian operator. This is an important difference, and moreover not making it tends to obscure the meaning of the Schrodinger equation, which is deeply related to the idea of energy as the _generator of temporal translation_ in the same sense that momentum is the _generator of spatial translation_ , and in turn to Noether's theorem where that energy and momentum are the conserved quantities associated with homogeneity of the laws of physics with respect to both temporal and spatial translations (needs modification in General Relativity). The "real" operator Ehat is Ehat = ihbar @/@dt, which essentially mirrors the momentum operator phat = -ihbar @/@x, and thus just as phat acting on psi gives you the increment needed to move a small step forward in space, Ehat gives you the increment needed to move a small step forward in time. The trouble is that Ehat is actually not a bona fide quantum operator but a "pseudo-operator" which acts on the _sequence_ of wave functions throughout time: the system Hilbert space technically only contains the (equivalent of) wave functions at each single point in time, so Ehat does not live in the set of operators on that space. Hhat, however, _is_ a bona fide operator, as it applies to the configuration at any one point in time only, and what the Schrodinger equation - now writeable as Hhat psi = Ehat psi - is telling you is that for a solution to make sense, Hhat must also translate it forward in time in the same manner Ehat must, that is, that a time evolution sequence is only valid if it was generated by the same operator that gives the energy at each individual instant. In relativity theory, this notion of energy also shows up, too: all particles have a forward time-directed "four-momentum" component and this relates to their energy. And moreover, tells you the true physical meaning of energy. Energy is a measure of the dynamism of a system or object, and this also explains its role as "nature's money": to make things happen (dynamism) you need some of that dynamism-maker, i.e. energy. It is interesting also that one has to go outside of Newtonian mechanics to find this in its fully appreciable form, despite that the energy concept also appears within it.
yes, that's what I think... just because at t=0 the E-hat operator turns to be multiplication by a constant, that doesn't mean that at arbitrary t, the effect of the operator will be the same. At least I'm not sure that can be concluded by what has been said at that point. Also, assuming that, the resolution of the differential equation also is not correct... psi(x,t) = (i*h/E)(d/dt)psi(x,t), then the solution should be psi(x,t) = exp(I*h*t/E) + c(x), where c(x) is an arbitrary function of x, that can be obtained by the initial condition of psi(x,0). Not sure how the solution ends up being multiplied by the initial condition.
@@user-uu9dm5pz7z Not that you should care particularly, it's irrelevent to QM, but classical liberalism/soft anarcho-capitalism isn't very rightwing. Whilst I think free market capitalism is the fastest way to improve technology and thus quality of life and so in most cases is the best option, I also think that it is the responsibility of a state to provide high quality essential services like healthcare, education, emergency services, and prisons etc. that are free at the point of access, funded by taxes. There are alot of important exceptions where market trends are natrually harmful to everyone. My social liberalism is clearly more 'important' than my slight econmic right-of-centre leanings. Basically don't claim me for your side, if I was American I'd have voted Biden.
@@AlexMcshred6505plus 10 months ago is a long time in politics for me so I wouldn't associate myself back then to now. Besides economic conservatism and social liberalism is left wing in my view which is where you align. I loath social liberalism but I believe in regulating giant corporations to ensure that they do not have too much power which a lot in the GOP and the GOP leaders like to call pure socialism. But if these companies are to dictate/control a nation that is more powerful than the government, I think an entire free market should be limited to free market for an average citizen.
Holy crap, thank you for admitting that there was a serious contradiction in the time evolution according to Copenhagen. I have been trying to express that problem to physicists and get an answer about it for *YEARS*. All I get as a response is "shut up and calculate", or a restatement of the Copenhagen position that solves nothing, or they'll take my question down. They have tried to convince me that I'm crazy or dumb or irrational for seeing it as a huge problem. While you haven't made it make sense in this lecture, it's so nice to know that I am not the first moron to find Copenhagen deeply unacceptable.
Several times, Prof Adams said that the wave function was completely descriptive of the state of a quantum system, however mass repeatedly appears in the equations he is using, and appears not to be described by the wave function itself. I am aware this question likely touches on more in depth topics, but if someone could explain at least the basics of what appears to me to be a contradiction, it would be greatly appreciated
how can he modify the linear schrodinger equation into non linear just by adding the probability term in schrodinger equation?does this fit the values in the equation?
Operators....wtf.....dmas...coefficients...factors...? Eighen value at that time position Eighen function is prediction of the motion of wave(approximation ifnoatrice movement?) Total Schrödinger solution???
CAN SOMEBODY EXPLAIN why the exponential was introduced at 46.16 when the derivative was evaluated . i have a feeling that it's something super simple but still can't wrap my head around that .
The differential equation says that time derivative of psi is a multiple of psi itself. Only function that satisfy that condition is that psi is exponential function of time.
+Aleksi Dragoev No, it results from the dispersion relationship of the electromagnetic wave equation (sounds complicated but isn't just wiki it). As mentioned, it isn't a constant but indeed it has an upper bound in vacuum c = (mu0*epsilon0)^-1/2. Basically the value is set to handshake the wavelength and frequency of a wave.
+ForsakenRainMan527 It's because the term (-iE over h bar) is a constant, he also says it at some point. The equation is of the type y(x)' = a*y(x), that's the derivative is the function itself times a constant. And the only functions that satisfies this is the e function. The solution of y'(x) = a*y(x) is y(x) = e^ax. (You can check taking the derivative of y = e^ax, that's y' = a * e^ax = a*y.)
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then! He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
14:06 "the time rate of change of position of a particle is the gradient of the force." Which is wrong. It's the gradient of a potential, or you can call it an acceleration or force per unit mass but it is not the gradient of a force. You cannot take a gradient of a vector. It doesn't mean anything.
I'll just help you out by saying that starting with a real number, if we keep self-multiplying, the output can grow or shrink exponentially. With complex numbers, we get rotation in the complex plane along with exponential decay or growth in the magnitude. When we start with a magnitude of 1, we only rotate, which is physically embodied by a simple harmonic oscillator. A quantum simple harmonic oscillator starting at an energy eigenstate is basically infinite simple harmonic oscillators running in parallel (which we capture with Psy(X,t) using X to address each possibility of simple harmonic oscillation). If you do not start at an energy eigenstate, then the prof suggests describing the initial conditions as a linear combination of energy eigenstates and using the fact that linear combinations of a solution to the Shrodinger equation still yields a solution. The same trick is used in classical mechanics to model vibrating systems with many wavelengths among the underlying modes of vibration. So while I would say "not knowing about harmonic oscillators will make this course hard" I also say that the concept is probably a lot simpler than you are afraid of :)
![Noob To Max With DRAGON REWORK In Blox Fruits [FULL MOVIE]](http://i.ytimg.com/vi/LnBMOinoOvA/mqdefault.jpg)
His enthusiasm makes me want to learn so much more
thats your problem
good
Neel Modi physics is interesting. Mathe instead...you keep them down that hall XD
Amen. Plus he does have an infectious smile.
Yeah true..
love the way professor Adams explains things, i'm starting to get my master degree in physics and yet by watching these lectures i feel the need to study more,it's like MIT courses makes you realize you need to learn more and more and more... and it's never enough!!!thank you MIT opencourseWare for giving me the opportunity to experience quality courses with these great guys. love you
Did u get it?
xxlblackyoung seconded
@@xxlblackyoung No, of course not. He is just pulling your leg. He is completely clueless. :-)
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@@gaanabajana9343 What's with the spamming?
I'm just jealous of these guys' ability to ask interesting questions that seem so logically connected to the subject but i could never come up with.
I'm jealous too but I can ask that kinda question. Maybe the guy has remembered them before.
Although they are smart, they may not be as smart as you think.
Most of these guys studied QM either on their own (e.g. reading books like QM for Dummies or watching RUclips etc) or took QM course before arriving at MIT. Yes indeed, there are schools that give introduction to QM in High School. So, if they have done that, they are pretty smart.
But realize this may not be the first time they are seeing this. So, smart indeed. But maybe not quite as smart as you might want to believe.
Working the problem sets and the readings help a lot in that regard.
As this is on OCW you have open access to the lectures, recitations, and problem sets as well. If you really want to learn quantum mechanics I highly suggest you look into this wealth of information.
Congratz to the man doing his best to manage the input volume so we can hear the questions ^^
what i like about his method is that he clarifies all the subtle points so that you don't have anything unclear in your head
This instructor is worth his weight in platinum!! He is FANTASTIC concerning this somewhat obtuse subject. I am impressed beyond words.
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
The teacher in the clip is very nice - patient, and down to earth.
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Wish he was my lecturer when I studied this. Makes it so interesting, relevant and clear.
Good job man
Lies again? Samsung Ericsson
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These guys always ask very good questions...
Nope, but he encourages them to ask. would you him to say, '' that's a boring question, never ask again!''?
Excellent question as always 😂
He is also very good at understanding what really the listeners would get confused.
No question is a bad question if you are really confused about it. You just need to ask.
@@Saptarshi.Sarkar Yes we totally get that but what he means i guess and i agree with him on that, is the fact that so many questions asked in that class improved my understanding of the concepts, like every question was necessary, without those students this class wouldn't have been the same and the prof was brilliant at understanding the questions as well as elaborating and answering them. It's like everyone in that class played a role in teaching.
As a holder of a computer science degree and another in electronics I bow to the recognition of reality. Circuits and code only do what they are made to do as does your world. So cool. Thanks for the pump.
Thank you very much for making these lectures public. Great topics and explanation !
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Really good explanation - excellent lecturer (Allan Adams); he actually invites questions, repeats them and then gives cogent answers.
It's the first time I've seen someone explain the relationship between eigenstates and Schrodinger's equation. Also how superposition falls out and is effectively a consequence of 'stationary states', therefore unaffected by time. This creates a physical distinction between the quantum world and the classical world, as he explicitly demonstrates; the interface being the 'collapse' of the wave function or 'decoherence' as he calls it, when superposition disappears. Since the wave function is 'all you need' and SE is 'not derived, just posited' makes me think it's a good candidate for the 'God' equation, meaning it fundamentally describes everything that's yet to come into being.
binging QM lectures, so much better than Netflix
These really are great lectures. I'm using them to supplement my coursework and they're really helpful in giving meaning to the equations and solutions i derive in my homework. For instance, I have a midterm tomorrow and i feel pretty good with my ability to handle the math and solve problems; but if asked what my solutions imply i would be hard pressed to answer without the intuition i gain from these vids. This lecture series really helps build my understanding of the material.
Thanks MIT OpenCourseWare!
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
@@pompookgantsu2286 maybe you should just get some more brain cells and learn it yourself.
Stellar professor, excellent lecture. I have studied physics myself and got really frustrated. I know everything there is to know about boring physics lectures. This one is motivating, interesting and entertaining. Big up for Professor Adams.
Nice Lecture
Take a shot every time he picks up his bottle and doesn't end up drinking from it haha. Amazing prof.
hahaha
he is a good prof of quantum
"mathematicians are sneaky. that's why we keep them down the hall." XD
Valen Cheung that’s what you learned
24:20
Anyone else transfixed on what he is drinking and how he transports it around the room without ever taking a sip?
Who says it's a drink?
Gregory Whittington thats coffee n either milk or carnation creamer
You have observed a macroscopic quantum mechanic event in action.
i wasn't, but now i am
The explanation and the answer of the question around 57:00 was excellent.
11:00 explanation of wave function collapse 12:00 what happens next? 14:30 hook 15:30 good q
18:00 personal note
29:00 non deterministically by probabilities collapse
30:00 !!!!
33:00!!!!
44:00 probability of E !!!!
46:00
51:00
58:00
1:03:00
1:04:00 continuous k
MIT is so awesome that I really want to study there!
you are already studying
Kristian Factora haha
Why
34:26 did you guys notice that chalk trick
Concerning the discussion of infinite combinations of continuous functions becoming discontinuous at 24:38 I would just add that while it seems merely theoretical it provides further evidence of quanta. We have must have exactly so many wave functions interacting or we can break things like smoothness and continuity which match closely with observation. Limiting behavior defying observation is also what led to the ultraviolet catastrophe, another artifact of quantization.
Nope.
17:43 "A piece of chalk that I am treating as a quantum mechanical point particle." Physics textbooks in a nutshell.
For those already initiated in QM I repeat here some comments previously made to similar videos. They may clarify debatable points.
The Schrödinger time dependent equation (STDE) when applied to a wave representing an initial state of, say, an electron bound to a proton and together forming a hydrogen atom, predicts and retrodicts all the future and previous states of the electron wave, in the same fashion than the evolution equations of classical mechanics predicts the movement of the Earth around the Sun. Note that the STDE is energy conservative, that is, the initial state as well as the predicted and retrodicted ones all have the same energy.
As is well known the bound electron has a completely different conduct. Whatever the initial state and in absence of other interactions an excited electron will settle in a stationary state radiating energy (in the form of a photon) along the way. If the stationary state is the ground state the electron will stay there forever (in absence, as said before, of other interactions). Otherwise the stationary electron state is ephemeral and will be abandoned to radiate a photon and assume a new stationary state of even lower energy. This "down the staircase" process repeats until the ground state is reached. There is no manner to adapt the STDE to this physical process. This inconsistency was discovered by none other than Niels Bohr, as can be inferred from the report of Werner Heisenberg. See our note
www.researchgate.net/publication/356193279_Deconstruction_of_Quantum_Wave_Mechanics
After discovering the tremendous inconsistency it would have been natural to announce that the STDE contradicted with physical facts, and ask for a correct equation. I assume as true, but only know from hearsay very long ago, that in Einstein's viewpoint the correct deterministic time dependent wave equation had to be non-linear. References to this historical detail would be appreciated.
It is hard to believe but, against reasonableness and common sense, Bohr decided to adopt the STDE as correct and that continuity, causality and determinism of physical processes were wrong because they contradicted the STDE. Apparently mathematical equations on paper were more relevant than the experience of the whole human race. Then a series of new and fanciful "quantum physical principles" were adopted.
In my opinion the powerful quantum establishment dogmatically defends Quantism and strongly rejects any attempt to correct its misdeeds, even if the correct deterministic time dependent wave equation available.
With best regards to all.
Daniel Crespin
That's utter bullshit. Even a cursory look at the Schroedinger equation tells you that it is not energy conserving.
Wonderful lecture - manages to work at both the intuitive level and the algebraic level. Thank you!
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
Nice, I can listen to this and not get an headache! Main principles respected, thank god!
22:00 So, why are the superposition principle and linearity different from each other? How can you have a linear wave equation without your wavefunctions obeying the superposition principle? How can the wavefunctions obey the superposition principle without the equation of which they are solutions being linear? Are we making a pedantic distinction between physical properties of a system and the mathematical properties of the equation that describes that system?
tokamak An example of a nonlinear equation that has the superposition principle in it:
sin x = 0
It is nonlinear (as you can readly tell) and its solutions are integer multiples of pi (neatly already homogenous) when considering just the real numbers. If you sum two solutions (equal or different) you get... Another solution. And that is additivity or superposition, at least in a very simple way.
If y and z are two of the solutions of the equation above, one can clearly see that:
sin (y+z) = sin(y) cos(z) + sin(z) cos(y)
Because always when sin(x) = 0 => cos(x) = 1, implying, for instance:
sin²(x) + cos²(x) = 1.
Then:
sin (y+z) = sin(y) cos(z) + sin(z) cos(y)
= sin(y)*1 + sin(z)*1
= sin(y)+sin(z) = 0+0 = 0
As you can see superposition DOESN'T imply linearity. But the converse is true - even if there is no proof here, there is plenty of it elsewhere.
Notice, however that this property doesn't apply to all x in our example (just the solutions, which seems to be good enough) and that it is not homogenous for all x in our example for similar arguments, even if homogenous for all solutions - and that seems, again, to be good enough.
So superposition and linearity are different properties from each other, even if they are somehow related to each other. You can't have a linear equation without the superposition principle, but you can have a nonlinear equation WITH the superposition principle. We are not making a distinction between the properties of a system and the mathematical properties of the equation (but that is not physics or math, it is philosophy: some scientists would say you should make such distinction - Bohr would say that, actually - and other wouldn't); they are different properties.
But your third question, I think, is not answered. What nonlinear wave equations with superpostions as its solutions can exist? I don't think we really KNOW the answer to this question.
I've seen some examples of nonlinear equations with a superposition rule or a superposition principle even. But I don't know of any equation like that in quantum mechanics (I'm not an expert in nonlinear equations, though, and I think one could readly say that as well).
So it would be interesting if somebody could tell me about some examples concernig such topics, just for curiosity - what I readly checked, in a quick search, was not entirely satisfactory or conclusive for me in that matter.
to use a schrodinger equation first the superposition disappears and the wavw function collapses to a single one. so because the wave collapses i believe it needs not support the superposition principle.
Is there a video somewhere introducing the math into quantum physics? I like the abstract stuff, but when it comes to the equations, I'm totally lost.
+Tom Franse The prerequisite math listed in the syllabus is 18.03 Differential Equations (or 18.034 Honors Differential Equations). You can find the MIT OpenCourseWare version of 18.03 at: ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011
Thanks!
+Tom Franse It's amazing how much easier this material becomes once you've had linear algebra and differential equations. I watched some over one summer and was just floored at how "hard" the subject was. Took those math courses now it's no problem at all.
questions? when is the first exam? there's one in every class...
For anyone who would like introductory visual representation of the linear algebra, this link is from Yale's BioChem-101 lecture introducing the Schrodinger equation: ruclips.net/video/B4VSqAB_JcU/видео.html
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then!
He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
Love MIT OpenCourseWare
I really like this guy!
Me either
You can also get some idea of the "decoherence" problem by determining the TYPE of infinity that the solutions can fall into when this occurs. Is it the smallest COUNTABLE infinity (Aleph Null in Cantor's system) -- the "rational numbers" -- or some higher infinity, such as the number of points on a line, "C" (called this because there is no proof that it is the next-highest type of infinity, though to my knowledge there is nothing between Aleph Null and C), which is, I think, the 'real numbers"? The former has separate, discrete values and the latter does not (its members flow smoothly into one-another with no "edges"). It seems to me that the former has to be true since all observers looking at a given result in a given universe see the same result, while the latter would allow somebody somewhere in that same universe to see a different result (slightly different or perhaps even very different), since the are no rigid "edges" (gaps between) to the values observed.
A genius can be defined as someone who can redefine the obvious in such a way so as to return something of value that is beyond those who do not understand on this said genius level. This guy nails and proves it. People at work are getting tired of me telling that everything reduces to waves, probability statistics and magic, pure “fing magic”. Not a student but I love this stuff. Don’t stop.
It’s that great full dead juice.
The partial with respect of time of a wave function \psi(X,0)?
52:30 Ok, what gives here? Stationary position for a particle. As soon s I measure position, I know the positin exactly. Therefore momentum is completely undetermined. Therefore it's almost certainly going to move - the probability that's momentum is zero, which it must be for it to remain stationary, is nil. So how can a particle ever sit still *when we know where it is*?
To be honest, this is such an amazing lecture like we too learn quantum mechanics in class but it seems like those students that are asking questions know more than my teacher.
explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
Hmm I am not that good in quantum mechanics that I should fully understand the whole lecture, but how much I got it's that here he tells about when a system evolves it means with respect to time, for that we use shrodinger equation while it is rich in concepts like you just can't precisely measure two non-commuting quantities , it gives that probabilities but not an exact number. When he talks about the eigen value , where he tells about superposition of states ,and so many more
@@pompookgantsu2286 Time is that which the clocks show. We tried to explain that to you when you were five or six years old and then again when you were in high school.
@@schmetterling4477 omg this again LMAO you have no clue of what this video is about do you?
Just for once I want him to say "that's actually not a very good question".
I've some questions regarding this lecture.
1. If the momentum is variable in nature during travelling of any object, then what could be the predictable approximation of Schrodinger wave function ?
2. If the time gets collapsed or the time starts to run backward, I mean reverse, then how the wave function can be expressed ?
3. As severally we read the time gets stopped inside the black hole, then can we really call a particle existing inside the black hole, as in eigen state ?
** If not so can it be possible to apply the time variant wave function at that place for computing energy ?
*** If really we can't apply the time variant wave function, then is it true that the wave nature of any object disappears inside the black hole ?
1. Magic 2. Sorcery 3. Witchcraft
The statistical outcomes are based on the perspective, taken at the time of measurement. Perspective is similar to a geometric angle.
at 45:00 partial derivative of function at t=0 with respect to time,isn't that supposed to be equal to zero?
I know you're long past this question but this answer is for anyone else with the same question. What if the function is e^t? The time derivative of e^t is e^t, right? So the time derivative at t=0 is 1. That is, if Psi(t)=e^t then Psi'(0)=1.
We have to look at what the function is. Usually the time-dependent part of the schodinger equation is given by something like Psi(t)=e^(-iEt/h) so we would NOT get 0 if we took the time-derivative at t=0.
Now, what if Psi(t)=e^(-kt)? Then Psi'(0)=-k.
Etc. etc.. etc..
In other words what he meant is: first take derivative of psi(x,t) and then assign t=0.
Its exactly as Александр Багмутов says.
@@АлександрБагмутовHow about the following step? That equation only applies when t=0, why did he extend this to all time t? 46:00
@@dr.merlot1532 That equation only applies when t=0, why did he extend this to all time t? 46:00
We discussed that we can-with superposition of Eigen state Schrodinger equation solutions make approximately solution to the Schrodinger equation for any state, where the coefficients are the norm squared of the probabilities. Does it make sense in any way to map those coefficients into something like a maclaurin series-so like for each value of the nth derivative (n is an integer) of the function you get a coefficient, with everything else equaling to zero? - to account for the collapsing. But the problem with that would be we won't know which coefficient corresponds to which collapsing. So maybe we could take combination (product) of all such derivatives in all terms-but each degree of derivative evaluated at a different value than every other in a term and than the same variable in every term-in such a way that the symmetry takes away every term other than the one or two that we are able to compute. The combination of all possible degrees of differential functions would mean-okay take everything else as constant and how does this change-remove thay-now everything else as constant and how does this change and so on. While the equation itself would be very long to write down unless someone finds a clever approximate non-polynomial function -but we can still clearly be able to identify the terms that don't cancel out.
Is this the formulation of Max Born interpretation-so that the series continues to exist even after measurement.
At 48:10 the ability to convert between energy and momentum is situational, is it not? That is, not all energy would be equivalent to momentum but we can do so in this problem due to the location of the particle being the aspect of the state we are evolving over time?
Kinetic energy and momentum always form a four-vector. They can not be separated because of relativity.
@@schmetterling4477 Thank you for your reply. That confirms I’m misunderstanding what the nuclear engineering lectures on here are saying about energy transfer being affected by the momentum of the particles in question
Newton's equation F=ma is not "just posited." You can derive it using an action principle involving the Lagrangian. Where is the corresponding process for Schrödinger's equation?
46:00 is that wrong? That only applies when t=0. Why did he make such big change?
45:36 that equation is nothing more than f'(0)=c where c is a constant. It is just a initial condition. How could he get the following equation at 46:00?
46:00 Here I think he used his conclusion (what this tells me is that under time evolution, a state which is initially in an energy eigenstate remains in an energy eigenstate with the same energy 46:51 ). He did not prove this conclusion. He used his conclusion as his assumption in the process to obtain this conclusion.
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then!
He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
I took QM as an elective course in my electric engineering program. I can guarantee that if you had a solid core courses in calculus, diff eq, vectorial calculus and stochastic methods you will succeed and be just fine. I can define QM as a probabilistic method of understanding classical physics and in my opinion is what really happens in our everyday world. Good luck to the ones that are completing the course today. If I can help just let me know. Regards and good luck
10:30 he says we can only measure eigenvalues on measurements. Doesn't that imply 100% certainty in that observable?
This depends on the state you are measuring. If you measure a quantity for which you are in an eigenstate of the corresponding operator, then yes, you are 100% sure that the measurement will give you the corresponding eigenvalue. However, you can also have a state made of multiple eigenstates of the observable you are trying to measure. In that case, all you can say is what is the probability of getting a particular eigenvalue, which is given by the absolute value squared of the corresponding expansion coefficient.
At 48:37, "Does the energy change over time? No." Entropy?
At around 14:07 Dr. Adams says, "The time derivative of position is the gradient of the force." What does he mean by this? Did he misspeak here? First of all, forces are vector quantities, so you can't take gradients of force functions (only divergences or curls). Second, even if you took, say, a one-dimensional ordinary derivative for Force=F(x), how would that give you velocity? I'm confused...
Jamin Kidd I think he meant the gradient of the potential energy!
ricomajestic Yea, I figured he was referring to conservative forces being the gradient of a scalar potential. I suppose it was just a mistake!
50:45 why did he say that probability is whole function squared, when Postulate no 3. says it is only coefficient (in this particulare case exponential function) that should be squared to get the probability?
The system is in a pure state. There is only one coefficient.
47:37
shouldnt the schrödinger equation have parameter (x,t) instead of (x,0) at second row?
Yes. Only in the wave function in the LHS.
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then!
He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
superb.. this professor REALLY LIKES his job. Unlike many professor in INDIA
The electrons in an atom are in stationary states. Atom is highly stable structure
I love how the professor's level of passion for the field grows as the class progresses; clearly amped by the class grasping these counterintuitive and gorgeous mathematical models. It makes me nostalgic for those few short years of intense study, when you could pay to learn what you wanted to learn, in such a focused professional way; several radical departures from the first 12 years.
Is there a way to get the problem sets? I would very much like to read them
MrArthur0920 The problem sets and solutions are available on the MIT OpenCourseWare site at ocw.mit.edu/8-04S13
I forget how to multiply fractions from 5th grade, aside from that, where do I start?
Precalc then trig, calc 1,2&3 differential equations for physics, then take nuclear physics courses
something like would have to work out constants but using a seperation of variables with 3 functions, 2 of t, 1 of x?
but i started learning PDE last week and havent spent 24 hours since first lecture here...
f ~ exp{(a + bx**2t)}
Huge love and Respect to Professor from Pakistan
53:40 according to the law of conservation of energy hence universe is in eigenstate ?
but position change
The universe does not conserve energy. Try again.
So...operators only tell you the possible values of the measurement (eigenvalues) will be...
And so I base my argument to hold my thesis that time is equal to movement times distance and from here forward understand when I look upon a thing in physics thus be applied.
He is a brilliant teacher. Zwiebach is good too, but this guy is better.
I have a good question,first there was an experiment done where they watch atoms and in the experiment not sure but they could observes the result of atoms traveling trought light and they where all messy but when observes they where all " calm " witch does work with schrodinger the atoms are messy and calm at the same time BUT my question is get the experiment going watch it and observe , it will be calm after that some how time travel and with the same experiment in theory the result should be the same but if you don't observe it will those atoms will be calm or messy ? is ( easier explanation is would time travel affect the same experiment?)
Mit open course can make any physics student proud of himself
It's just phennomenal way of teaching
Thank you for sharing these videos !
I have studied the first one and I enjoyed them a lot !!
I love the way Quantum Mechanics is teached and the very positive atmosphere of these lectures.
I have found one explanation that didn't convice me.
This is at 46 min about, during the solving of Shrödinger Equation (SE). Indeed, SE is simplified by replacing Psi(X,t) by Psi(X,0) and by replacing Energy operator by Energy Eigenstate. This is strange to replace Psi(X,t) by Psi(X,0) under the time derivative symbol because the result would be 0 in that case ... I think that one could apply Shrödinger equation at time 0 instead and therefore replace Energy operator by Energy eigenvalue and find the solution around time 0, then resolve this equation at time Delta t and so on ... and conclude that general solution is the one that is given in this video (perhaps another more straightforward way is possible).
P.S.: sorry for my english, I am french ... nobody is perfect :)
teached naught - taught*
Let's say at an instant we express a wavefunction as a superposition of energy Eigen functions. How can we prove that the time evolution of the wavefunction is given by the sum of the time evolutions of the individual Eigen functions. He said we can do it, but how can we prove it. I mean what if a particular superposition is only valid of an instant. I was solving the Schrodinger equation to prove this, but I am stuck
Can someone explaint to me why in the last exemple k*L = pi(n+1) and not pi*n, L is positiv but why k couldn't be 0 since it is at the boundary and outside the box?
And what about the double slit experiment?
Whoever did the subs is a godsend
What will be Schroedinger's time independent equation for a bouncing ball?
Time as we perceive it seems like a side effect of our use of numbers.there are periods of time.if we evolved without numbers? Like a smart bird, would we be intelligent? Would we wonder of time?
best teacher everrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Doesn't observation...affect the thing being objected being in line wih each other..? Emitted ...?
Observation is irreversible energy transfer.
what, if anything, is the effect of electron mass of the time evolution? presumably the electron cannot travel faster than the speed of light, so does the mass set conditions on how much space an electron can travel in time given a certain energy value?
malaise69 In quantum mechanics the electron mass is always the rest mass, at high energies you should take into account relativistic effects then change the theory to relativistic quantum mechanics or even more to quantum field theory then the electron now becomes a field and the mass is only a parameter of the theory.
So, half way I say time is adjustable through observation. Matches the philosophy that we create what do observe. I’ll be back to edit. Decoherence is an optical term.
Can you tell me how to ignite a bunsen burner?
Carefully.
I think 46:00 is WRONG. First, he needs to assume that the E-hat operator doesn't concern t, in order to get the bottom-left equation. Second, the bottom-left equation is evaluated at time 0, he shouldn't just extend it to any time t without a proper argument, and obtain the bottom-right equation. I don't think I can trust the lecture series any more.
The operator he calls "Ehat" is actually "Hhat", the Hamiltonian operator. This is an important difference, and moreover not making it tends to obscure the meaning of the Schrodinger equation, which is deeply related to the idea of energy as the _generator of temporal translation_ in the same sense that momentum is the _generator of spatial translation_ , and in turn to Noether's theorem where that energy and momentum are the conserved quantities associated with homogeneity of the laws of physics with respect to both temporal and spatial translations (needs modification in General Relativity). The "real" operator Ehat is Ehat = ihbar @/@dt, which essentially mirrors the momentum operator phat = -ihbar @/@x, and thus just as phat acting on psi gives you the increment needed to move a small step forward in space, Ehat gives you the increment needed to move a small step forward in time. The trouble is that Ehat is actually not a bona fide quantum operator but a "pseudo-operator" which acts on the _sequence_ of wave functions throughout time: the system Hilbert space technically only contains the (equivalent of) wave functions at each single point in time, so Ehat does not live in the set of operators on that space. Hhat, however, _is_ a bona fide operator, as it applies to the configuration at any one point in time only, and what the Schrodinger equation - now writeable as Hhat psi = Ehat psi - is telling you is that for a solution to make sense, Hhat must also translate it forward in time in the same manner Ehat must, that is, that a time evolution sequence is only valid if it was generated by the same operator that gives the energy at each individual instant.
In relativity theory, this notion of energy also shows up, too: all particles have a forward time-directed "four-momentum" component and this relates to their energy. And moreover, tells you the true physical meaning of energy. Energy is a measure of the dynamism of a system or object, and this also explains its role as "nature's money": to make things happen (dynamism) you need some of that dynamism-maker, i.e. energy. It is interesting also that one has to go outside of Newtonian mechanics to find this in its fully appreciable form, despite that the energy concept also appears within it.
yes, that's what I think... just because at t=0 the E-hat operator turns to be multiplication by a constant, that doesn't mean that at arbitrary t, the effect of the operator will be the same. At least I'm not sure that can be concluded by what has been said at that point. Also, assuming that, the resolution of the differential equation also is not correct... psi(x,t) = (i*h/E)(d/dt)psi(x,t), then the solution should be psi(x,t) = exp(I*h*t/E) + c(x), where c(x) is an arbitrary function of x, that can be obtained by the initial condition of psi(x,0). Not sure how the solution ends up being multiplied by the initial condition.
Exactly, I don't get, how can that be true. I was searching the comment section. It seems that noone has noticed it!
'...my life is easier if i don't think about curvy bottoms...' lol (@ 1:15:09)
good catch
Right wingers unite! #wearetheresistance
Spoilt child!
@@user-uu9dm5pz7z Not that you should care particularly, it's irrelevent to QM, but classical liberalism/soft anarcho-capitalism isn't very rightwing. Whilst I think free market capitalism is the fastest way to improve technology and thus quality of life and so in most cases is the best option, I also think that it is the responsibility of a state to provide high quality essential services like healthcare, education, emergency services, and prisons etc. that are free at the point of access, funded by taxes. There are alot of important exceptions where market trends are natrually harmful to everyone. My social liberalism is clearly more 'important' than my slight econmic right-of-centre leanings. Basically don't claim me for your side, if I was American I'd have voted Biden.
@@AlexMcshred6505plus 10 months ago is a long time in politics for me so I wouldn't associate myself back then to now. Besides economic conservatism and social liberalism is left wing in my view which is where you align. I loath social liberalism but I believe in regulating giant corporations to ensure that they do not have too much power which a lot in the GOP and the GOP leaders like to call pure socialism. But if these companies are to dictate/control a nation that is more powerful than the government, I think an entire free market should be limited to free market for an average citizen.
Operators wear a hat. The prime operators in quantum theory wear a top-hat.
Don R. Mueller, Ph.D. What’s a prime operator ?
Holy crap, thank you for admitting that there was a serious contradiction in the time evolution according to Copenhagen. I have been trying to express that problem to physicists and get an answer about it for *YEARS*. All I get as a response is "shut up and calculate", or a restatement of the Copenhagen position that solves nothing, or they'll take my question down. They have tried to convince me that I'm crazy or dumb or irrational for seeing it as a huge problem. While you haven't made it make sense in this lecture, it's so nice to know that I am not the first moron to find Copenhagen deeply unacceptable.
The best part of this lecture is how he could never drink his coffee
Several times, Prof Adams said that the wave function was completely descriptive of the state of a quantum system, however mass repeatedly appears in the equations he is using, and appears not to be described by the wave function itself. I am aware this question likely touches on more in depth topics, but if someone could explain at least the basics of what appears to me to be a contradiction, it would be greatly appreciated
Mass is energy.
@Maria H exactly
How fo you know when you have complete knowledge of a system if there are unknown unknowns?
That's the point. Complete knowledge in a classical sense does not exist.
Tienen uds un servicio de traducción simultánea?
Why did you delete the translation??!😢😢😢⬆️⬆️
how can he modify the linear schrodinger equation into non linear just by adding the probability term in schrodinger equation?does this fit the values in the equation?
pawan poudel He suppose that to answer a question
but in order to answer a particular question ,can we modify the equation?
It fits, is the point. Great lessons
I THOGHT I WAS KILLING TIME ! BUT TIME WAS KILLING ME !!!
what is present continuous
Great lecture
Operators....wtf.....dmas...coefficients...factors...?
Eighen value at that time position
Eighen function is prediction of the motion of wave(approximation ifnoatrice movement?)
Total Schrödinger solution???
CAN SOMEBODY EXPLAIN why the exponential was introduced at 46.16 when the derivative was evaluated . i have a feeling that it's something super simple but still can't wrap my head around that .
The differential equation says that time derivative of psi is a multiple of psi itself. Only function that satisfy that condition is that psi is exponential function of time.
@@ishankumar6473 that nakes sense . thanks
Here's a philosophical question: is collapse of the wave function linked to the second law of thermodynamics?
LReBe7 YES or at least I think so too. Why do we never hear about this? Collapse is NOT reversible!
It's interwoven with entanglement, which is closely linked to entropy. So yes
1:15:09 I hear you, bro.
Is the speed of light in a energy eigen state, because its *_"Constant"_*?
+Aleksi Dragoev Speed of light is not constant.
+Aleksi Dragoev No, it results from the dispersion relationship of the electromagnetic wave equation (sounds complicated but isn't just wiki it). As mentioned, it isn't a constant but indeed it has an upper bound in vacuum c = (mu0*epsilon0)^-1/2. Basically the value is set to handshake the wavelength and frequency of a wave.
Can anybody explain how he solves the equation at 46:10?
+ForsakenRainMan527 It's because the term (-iE over h bar) is a constant, he also says it at some point. The equation is of the type y(x)' = a*y(x), that's the derivative is the function itself times a constant. And the only functions that satisfies this is the e function. The solution of y'(x) = a*y(x) is y(x) = e^ax. (You can check taking the derivative of y = e^ax, that's y' = a * e^ax = a*y.)
+Gwunderi25 I think the professor solves it by first order linear differential equation.
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then!
He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
14:06 "the time rate of change of position of a particle is the gradient of the force."
Which is wrong. It's the gradient of a potential, or you can call it an acceleration or force per unit mass but it is not the gradient of a force. You cannot take a gradient of a vector. It doesn't mean anything.
+Bart Alder
Wouldn't it just be the integral of force on mass? As "rate of change of position" is just velocity.
Hi Kale Crosbie, am sorry to say that I still have no idea what they are trying to say, but thanks for responding.
I don't think it was anything rigorous, he was just pointing out that functions are typically non-linear in classical mechanics.
Thanks Kale!
Bart Alder yeah i think it was flip from his toung nothing serious
Real food for thought
Can I continue watching if I don’t know about harmonic oscillator?
I'll just help you out by saying that starting with a real number, if we keep self-multiplying, the output can grow or shrink exponentially. With complex numbers, we get rotation in the complex plane along with exponential decay or growth in the magnitude. When we start with a magnitude of 1, we only rotate, which is physically embodied by a simple harmonic oscillator.
A quantum simple harmonic oscillator starting at an energy eigenstate is basically infinite simple harmonic oscillators running in parallel (which we capture with Psy(X,t) using X to address each possibility of simple harmonic oscillation).
If you do not start at an energy eigenstate, then the prof suggests describing the initial conditions as a linear combination of energy eigenstates and using the fact that linear combinations of a solution to the Shrodinger equation still yields a solution. The same trick is used in classical mechanics to model vibrating systems with many wavelengths among the underlying modes of vibration.
So while I would say "not knowing about harmonic oscillators will make this course hard" I also say that the concept is probably a lot simpler than you are afraid of :)