I've watched some lectures of Professor Zweibach's course on quantum mechanics and by what i can say, barton's and allan's combination is probably the best anyone can have in their lives for QM, thanks MIT OCW, love y'all for providing this!
18:10 is an example of why this teacher is great. He doesn't just do some hand wavy crap or dismiss the question, but shows WHY on the black board. A teacher that can derive things from scratch is like GOLD
it goes both ways. some of my physics professors waste all of the lecture showing derivations, which is kinda useless because my textbooks already have the derivations and making the concepts clear to understand are the part the book lacks. a good balance between conceptual explanation and derivations is what makes this man such a great teacher.
Except there he was actually wrong because the dirac delta is not a function, hence the multiplication makes no sense at all in his definition. That said, the dirac delta is indeed an operator (actually it is a tempered distribution or even more specifically a compactly supported distribution), but it is defined as follows: delta_a(f) = f(a). It just becomes the evaluation of the function in the point a. I think what he meant was the integral of the product he wrote. In that case we can use the fact that the linear functionals (aka distributions) act on test functions by integral product (usually the notation is similar to that of L^2 inner product, or in L^p-L^q product, which exists by Holder's inequality). The integral is well defined by at least one of the two being of compact support (or well behaved at infinity) and that's ok. (I'm intending operator as in general term, the image space is obviously the complex field, hence functional would be more precise) I think being able to derive things on the spot is the bare minimum that an expert should be able to do if he holds uni lectures. Unfortunately there he was caught a little off guard.
never saw a professor was applauded at the end of the courses. but dr. zweibach certainly deserved this. the best lecture on this topic I have put myself in.
This particular episode is just epic. And I can kind of feel Prof. Adams's disappointment not being able to introduce the Schrödinger Equation himself in all its glory, having been laying its foundation for the last four lectures.
Thank you, MIT, for the value you put in us - self-learners, also thank you, for those who donate and make these lectures available for us. Hope I'll be listening to these lectures live as a student of MIT. Good luck to me! (I guess)
This is absolutely the PERFECT lecture for Schrodinger and I am so grateful for Dr. Z. He relates the math to the Physics, and makes sense of it all.. I need more :)
47:57 mathematicians were the first to work with abstract linear operators and infinite dimensional vector spaces, so I don't think you're giving them enough credit. Mathematicians don't think in just matrices.
mathematics is the study of all patterns. Physics is basically concerned with patterns observable in this universe. Therefore, he made a little mistake there! Whatever, Physics discovers is within the realm of mathematics
I know this is a little old but I'll add: his description is probably what you'd get from an undergraduate math student, and it's a totally legitimate first attempt to try to understand the situation. If you showed it to a seasoned mathematician the response might depend on their specialty, but many would probably recognize right away that in finite dimensions commutators have trace zero. An analyst would be unfazed (operator algebras are a major part of the subject). An algebraist might tell you about the Weyl algebra, which is something that some might describe as slightly "pathological", but not really for the reason he describes (for one it is simple but not semisimple, a confusing conflict of terminology). Nevertheless, the Weyl algebra is well-studied so it's definitely not something that mathematicians shy away from.
So the uncertainty of an operator is the standard deviation of that operator. It’s a measure of how spread out the probability density is from the maximum knowability or the mode of the pdf transformed by the operator.
I was just about to comment on the same thing. I've taken a full course of Linear Algebra but that explanation was better than anything i had in the LA course.
i have literally spent around an entire week.end downloading ALL lecture videos, lecture notes, assignments, exams, etc... for almost all courses... worth my time
Watching this a few times will eventually result a eureka moment of understanding not only how the Schrodinger equation works and can be derived, but also how it MUST be just so. It also takes the oft used term 'wave function collapse', and fleshes it out into how the measured observable (x, p or whatever) has to be an eigenvalue of the original wave equation, and it is modulated by an eigenfunction of the operator of choice. This lecture is presented with all the skill of a masterful prosecutor building up an unassailable case brick by brick, culimating with the 'got you'coupe de grace of crowning the E scalar value with its operative symbol, thereby unlocking the gateway to quantum wave mechanics. It is little wonder that the students give a warm round of applause at the end of this. But had they been able to fully digest the minutiae and nuances of this talk, it would have easily been a standing ovation. This is the quantum mechanics equivalent of the brilliant James Burke series of Connections from the BBC, or the equally as scholarly (but not quite so charismatic) Mechanical Universe presentations by David Goodstein from CIT.
+Ron Toolsie Did I get the last "genius coup" at the end (1:19:30)? Does putting a hat on top of E mean to "force" the energy to be quantized, to take only certain discrete values (the eigenvalues)? And (consequently) the other "observables" too? And if yes: isn't also the uncertainty principle hidden in this equation?It's an excellent lecture and Prof. Zweibach should indeed get standing ovations. I saved the video twice to be sure ... : )
at 1:00:10 them subtitles say 'Fourier told you you can't expand..." which is wrong (the professor didnt make that mistake, its only on subtitles); in fact Fourier 'told' us that we can expand any function as a linear combination of e^ikx.
He is very funny at 49:0 when he goes on about how mathematicians struggle with the most simple case of commutation. He is right... you can get an entire lecture called "functional analysis" about that problem and it's quite ingenious.
Amazing lecture. Well structured, clear and extremely engaging; it takes you on a journey where your knowledge and understanding of the topic progressively grows, but it's so balanced that it doesn't force anything on you.
That is only halfway correct. The problem with non-relativistic QM is that it is not a proper physical theory, but that is usually not being explained to you while you are learning it. One should, for instance, tell the student that the Schroedinger equation does not conserve energy, momentum and angular momentum and that the projection operator formalism for measurement balances this out in just the right way to arrive at the correct physical results for the kinds of systems that can be described by non-relativistic theory to begin with. That entire background is usually missing from QM 101 lectures, including this one.
As a matematician I beg to differ on what the professor said about us wanting to compute finite dimensional matrices. I think the most elegant mathematics is that of the infinite dimensional spaces that are behind this kind of phisics. I'm not at all scared by the fact that we are considering normed (or semi-normed) TVS and their duals without exhibiting any finite-dimensional basis for them, as long as I understand the underlying uniform structures and rigorously define what equality in the dual space means (i.e. weak equality on the test function space).
That's all cool, but you have to understand that physicists aren't giving a crap about any of that detail. For one thing we know that the SE is unphysical. It's a toy model that gets you exactly nowhere in real physics. For us the buck stops at the Dirac delta, which is the one line poor man's version of three hundred pages of functional analysis textbook. The stuff that we really care about (relativistic quantum field theory) is outside of the reach of serious mathematics for now as far as I know.
@@schmetterling4477 Oh, then I misunderstood what he was saying. I tought he meant "scary" as if we wouldn't want to deal with it, since I actually find it fascinating and that's why I'm all about it; but he probably meant it in the sense that we need to build a coherent theory which is sound and compelling, whereas for phisicists is more about the actual meaning of those quantities in their model.
@@giacomocasartelli5503 I also find functional analysis to be a fascinating mathematical discipline as it brings some sense of order into this infinite mess of functions. It just doesn't do much for physics because the problems with quantum mechanics do not stem from mathematical corner cases. They are deeply embedded in the core definitions of physics that all depend on a geometric substrate that we call "the physical vacuum". All our successes begin there, but so do all our failures. What needs to be exorcized is the notion of R^n as the underlying tangent space of reality. That's the end point and not the beginning, but for now we treat it as both and that's just wrong.
@12:09 I would have thought that the multiplication is the operator acting on a matrix and a vector. The latter one being the objects. Basically like this Mult(matrix, vector).
1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
35:07 energy operator V(x hat) ???? 55:00 energy collapses to eigenfunction psi_a 57:301:03:00 ?????? 1:12:00 ...... this is the operator that realizes the energy
Watching Mr. Barton Zwiebach's elegant explanation of deriving iħ ∂ψ/∂t = H^ψ (TDSE) and H^ψ = Eψ (TISE) is like going back in time to the first quarter of the 20th century and meeting one of the greatest minds in QM (Heisenberg in 1925 and Schrödinger in 1926), both of whom revolutionized physics with such cognitive cataclysm!
Anybody who shows you a "derivation" of the Schroedinger equation is performing a parlor trick for you. It can't be properly derived from anything, if for no other reason than that it's completely wrong. At most one could argue that it's a non-relativistic perturbation solution for quantum field theory, but I am not sure it's even that (you can see this because it doesn't include the Pauli exclusion principle, for instance, which should not drop out in a proper perturbation theory).
As a mathematician who has worked with the Weyl algebra I found his comments about mathematicians amusing, and quite wrong. There are things that mathematicians find difficult to understand in quantum mechanics since it has not been made rigorous but the Heisenberg commutation relation is not one of them.
John Smith I think he was just teasing mathematicians. Of course, mathematicians work with infinite dimensional spaces and hold seminars on operator theory all the time. If it weren't for mathematicians, physics wouldn't be where it is today.
He is just refering to the fact that the Heisenberg commutator requires the operators to be unbounded, the other one does not. This is what makes it more complicated.
1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
I'm Interested in the DIAGAGNOLIZATION of matrix EIGENVECTORS, and VECTOR using Taylor expansion and DETERMINANT for infinite series and PAULI MATRIX and Clifford Algebra for solving the Schoringer Equation And HEINGBER uncertainty for QUANTUM FIELD PERBUTATION
A couple of SiFi stories have "pointed out" that the Universe is a point, ie the Temporal POV IS Singularity property, that is the Philosophers "indescribable" temporal superposition spin-spiral function cause-effect of time duration timing modulation, we are Totality embedded in.., but cannot describe because it's "No-thing", e-Pi-i omnidirectional-dimensional connection by Pi-bifurcation Exclusion Principle that "floats" numberness in macro-micro, divergence-convergent, Vanishing point-positioning, ..and is the pure-math Superspin-spiral pivot of here-now-forever localization circularity.., the Condensed Matter and Theoretical Quantum-fields Mechanism of AM-FM In-form-ation substantiation that is the subject of the lecture. (By default?) If the lecture starts as it should with "known physical empirical laws" then this is the hierarchical dominance of phase-locked coherence-cohesion probabilistic pure relative motion logarithmic pulse-evolution differentiates in potential mathematical motion, possibility.., an Equation of this particular Timing-spacing integration wave-particle coordination-identification. By default, the Quantum Operator Fields Modulation Positioning Computation Mechanism is the only Actuality, in projection-drawing Perspective, Principle.
The build-up at the end is excellent! One question remains. He stated that Schrӧdinger Wave Equation is "deterministic." I cam cautious about accepting that but I would like to hear more about how it is deterministic.
The wave equation has no physical meaning. It's only when you calculate the probability function that you get real world implications. The wave equation will give you this probability function exactly. But, yeah, the probability function will never give you an exact answer as to the properties of a particle at a certain time. That is what I'm to understand anyway...
CrushOfSiel OK, but the wave equation describes the mathematics of momentum of the photon while the particle is the math of position. What it "really" is there is no one answer at this point.
I think the student meant his question about the delta function being an operator in a different way. Hes asked himself whether it even makes sense to multiply anything f with the delta function.
Yes, one can multiply smooth test functions with the delta function just fine. The mathematical difficulties that arise in non-relativistic quantum mechanics are only pathological from an exact math perspective. They are not actual physical problems. It gets much, much worse in relativist quantum field theory where divergences are NOT caused by poor use of mathematics. They are the results of real physical phenomena and they have to be dealt with accordingly by using proper physical intuition about why they arise and how one can still extract useful phenomenological results from the formalism despite them.
+David Gillooly It's a hermitian operator for a measurable in position x^hat, and it operates on the function to give you the position eigenvalue of the function. Kind of like having a continuity of infinitesimal kets and the operator gives you the eigenvalue of the ket. You can do that with most Potential functions as a measurable, this can be proven through taylor expansion as it acts on each variable.
5:48: "This operator acts to roughly give you the momentum of the particle." except, that, as we all know, ih*psi ' = E*psi. It DNE p*psi, and never has. I am confused why he thinks that.
Just answered my own question: When psi is taken as a derivative of time, then ihΨ ' = E*Ψ. When psi is taken as a derivative of displacement, then ihΨ ' = p*Ψ....
1:08:30 - I do have to say I disapprove of things just being "handed down from on high" to be taken on faith. Last lecture we got handed the momentum operator, and this lecture we're getting handed Schrodinger's equation. That's not really "teaching" - that's just training technicians. On the other hand, I stumbled across this paper a couple of days ago: www.researchgate.net/publication/328332637_How_to_Un-_Quantum_Mechanics It's simply AMAZING how thoroughly the writer derives so much physics from such a meager starting point. I'm still pouring over it, gradually absorbing more and more content.
Thanks a lot . I have a question : there are 2 energy operators !! One is the summation of the momentum and the potential operators , and the other is the one contains the partial time derivative !! Why :/ ?! I'm confused .
Ben Sama The first is the time-independent Schrodinger equation, which just calculates the energy eigenvalues of the eigenstates; the system as a whole is time-invariant and states don't evolve with time(stationary states). The second is the time-dependent Schrodinger equation which shows the time evolution of the states of a wavefunction when you don't measure a system to make it undergo collapse.
No, P(dx) would be meaningless. P(x) is the probability density at the point x - an ordinary function of x. The integral of P(x)dx over all x must = 1.
Best things of the universe are always hidden. They are not put up on advertisements boards or tv commercials. They are always discovered by keeping a meticulous perseverance. "Truth is not for all men but only for those who seek."- Ayn Rand Thank you Universe!
Very very good lecture. All the previous lectures was like isolat islands and focused to "draw attention to me I am hero" even the pirate theater target to the same. I think the fifth lecture by this gentlemen "great teacher" covered all the previous artistic plays. I think MIT may make a survey from different level of educated people like, those who know QM, familiar with QM or don´t know, to use the donated money on real lectures.
Unity-connection inclusion is operational Actuality, self-defining aspects of real-time Infinity as abstract Operators that specify a particular aspect positioning in Logarithmic spin-spiral Timing-spacing coordination, Fluxion-Integral Temporal superposition Calculus, and Qbyte line-of-sight identification of relative-timing density-intensity ratio-rates. Forward-Reverse lead-lag pastfuture potential now-> sync-duration, an abstract process of POV identification, is complex completion of vertices in vortices nodal-vibrational transverse trancendental condensation. This is the inside-outside orientation of Intuition required by Actual Intelligence before a student should attempt to rediscover a topic attributed to an application with personalised names. (Just saying) Fractal conic-cyclonic Superspin-spiral Superposition Totality Correspondence in time-timing Reciproction-recirculation Singularity positioning.., this is the inside-outside presence of holography, functional e-Pi-i Apature Observation.
1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
The expected value of p is based on the _square_ of the wavefunction, but since that is a complex function, to square it you multiply it by it's complex conjugate.
17:42 An MIT open course about Schrӧdinger Equation, I expected to get close to the universe's secret. But not that close... (I see what you did there)
I went to a Community College and my professor was at least as good as this guy. My professor received his PhD from the University of Chicago. So, you don't need to attend an expensive university to get a great education. It's what YOU put into it.
That's what he refers to when he says you can derive Schrodinger's equation using unitary evolution (or if you want to be picky the Feynman path integral is the formulation in QM of the principal of least action), but you can't prove unitary evolution you just take it as postulate. Just like you don't prove the principle of least action, you just take it as your starting point.
This was amazing lecture takes quantam mechanics to different dimension I can feel Prof Adams downcast on not able to introduce schorimder equation in it's full glory
1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
In the last video a guess was made that =∫lΨ(x) l^2·p(x)·dx. In this video, p(x) has been cleverly replaced, but lΨ(x) l^2 has also been changed to Ψ*(x). Does anyone know why? As far as I see it a complex number times it conjugate would give us lΨ(x) l^2, når just the conjugate alone.
I have one problem. Think about position, for example, everytime we measure an object, we get the same result. If the result that we measured is eigenvalue, why we always get the same result? (Does that mean that eigenvalue is unique?)
After the wave function collapses to a value a, you end up with AΨ = aΨ, in other words, after the wave function collapses, the measured value becomes the only eigenvalue. Any other eigenvalues before the collapse are now gone
Momentum being defined as mv only works for things with mass (and non relativistic speeds). Einsteins equation gives insight to this with E² = (mc²)² + (pc)². Setting m = 0 and solving for p, we get p = E/c = (hυ)/c = (h*(c/λ))/c = h/λ
Yeah but you need to do the operator on the wave function. According to what is on the blackboard you would get ∫hk dx = hkx from infinity to zero infinity. This is undetermined.
1 or unity concept of existence, the elemental principle of Logarithmic Time Communication and dominant floating prime point in even symmetricali-reflection of log base 2, square identity via the functional integration-differentiation operation of "e", the Inflation +/- zero-infinity distribution in which Pi bifurcation, fractalisation is Quantum-fields Mechanism Singularity positioning, holographic quantisation of implied potential pure relative motion and Algebraic Calculus of continuous metastable proportioning probability in creation connection. => e-Pi-i QM In-form-ation substantiation Operator. From Observation/Philosophy: "It's all ways Now", "All IS vibration", "Everything is connected" @.dt Absolute Zero Kelvin i-reflection containment phase-locked "mathematical" statements => real-time/sync of pure relative motion, formulae. (Thanks to the student who mentioned Dirac Delta Function, I have another conceptual equivalent to the idea of the cross-section of a string/axis in unit connection coordinates.)
I've watched some lectures of Professor Zweibach's course on quantum mechanics and by what i can say, barton's and allan's combination is probably the best anyone can have in their lives for QM, thanks MIT OCW, love y'all for providing this!
18:10 is an example of why this teacher is great. He doesn't just do some hand wavy crap or dismiss the question, but shows WHY on the black board. A teacher that can derive things from scratch is like GOLD
it goes both ways. some of my physics professors waste all of the lecture showing derivations, which is kinda useless because my textbooks already have the derivations and making the concepts clear to understand are the part the book lacks. a good balance between conceptual explanation and derivations is what makes this man such a great teacher.
Yes, he backs up everything he said with proof or examples.
Except there he was actually wrong because the dirac delta is not a function, hence the multiplication makes no sense at all in his definition.
That said, the dirac delta is indeed an operator (actually it is a tempered distribution or even more specifically a compactly supported distribution), but it is defined as follows:
delta_a(f) = f(a). It just becomes the evaluation of the function in the point a.
I think what he meant was the integral of the product he wrote. In that case we can use the fact that the linear functionals (aka distributions) act on test functions by integral product (usually the notation is similar to that of L^2 inner product, or in L^p-L^q product, which exists by Holder's inequality). The integral is well defined by at least one of the two being of compact support (or well behaved at infinity) and that's ok.
(I'm intending operator as in general term, the image space is obviously the complex field, hence functional would be more precise)
I think being able to derive things on the spot is the bare minimum that an expert should be able to do if he holds uni lectures. Unfortunately there he was caught a little off guard.
never saw a professor was applauded at the end of the courses. but dr. zweibach certainly deserved this. the best lecture on this topic I have put myself in.
The thumbnail really looks like he's fighting with QM
:D yes
Yes you are right
He’s standing face to face with the final boss
🤣
I really thought it was a meme or something lmao
I love listening to this professor. Even the hard stuff goes down easier with his friendly delivery.
This particular episode is just epic. And I can kind of feel Prof. Adams's disappointment not being able to introduce the Schrödinger Equation himself in all its glory, having been laying its foundation for the last four lectures.
This topic it's so hard and abstract but the professor made it look so clear, thats definition of a Genius , one who makes complex things easy
Thank you, MIT, for the value you put in us - self-learners, also thank you, for those who donate and make these lectures available for us. Hope I'll be listening to these lectures live as a student of MIT. Good luck to me! (I guess)
This is absolutely the PERFECT lecture for Schrodinger and I am so grateful for Dr. Z. He relates the math to the Physics, and makes sense of it all.. I need more :)
Where did you see physics here?
47:57 mathematicians were the first to work with abstract linear operators and infinite dimensional vector spaces, so I don't think you're giving them enough credit. Mathematicians don't think in just matrices.
However, it was an amazing lecture!
mathematics is the study of all patterns. Physics is basically concerned with patterns observable in this universe. Therefore, he made a little mistake there! Whatever, Physics discovers is within the realm of mathematics
I know this is a little old but I'll add: his description is probably what you'd get from an undergraduate math student, and it's a totally legitimate first attempt to try to understand the situation. If you showed it to a seasoned mathematician the response might depend on their specialty, but many would probably recognize right away that in finite dimensions commutators have trace zero. An analyst would be unfazed (operator algebras are a major part of the subject). An algebraist might tell you about the Weyl algebra, which is something that some might describe as slightly "pathological", but not really for the reason he describes (for one it is simple but not semisimple, a confusing conflict of terminology). Nevertheless, the Weyl algebra is well-studied so it's definitely not something that mathematicians shy away from.
This is the best lecture that I ever seen and it free. You helped many peoples. Very Clear. Bless you MIT.
So the uncertainty of an operator is the standard deviation of that operator. It’s a measure of how spread out the probability density is from the maximum knowability or the mode of the pdf transformed by the operator.
MIT professors are out of the world in explaining things making math speak out they are simply awesome
This was one of the most mind blowing lectures in physics I've ever seen.
masterful teacher.....and a substitute for another world class lecturer
Eigen functions and Eigen values explained brilliantly.
Are all the Professors at MIT so enthousiastic and smart?
24:30-25:00, the explanation of eigenvectors that I'd have paid 80,000$ for.
I was just about to comment on the same thing. I've taken a full course of Linear Algebra but that explanation was better than anything i had in the LA course.
Check out 3blue1brown's playlist on linear algebra.
Boi that's just the definition really
Dude, that's the definition... Av=λv
yeah it insane how he simplified it(not many people can explain eigen values,vectors,states)
Universe bless you MIT for making these invaluable lectures available to us. Thank you very much. My go to source for all my physics :)
*god bless
i have literally spent around an entire week.end downloading ALL lecture videos, lecture notes, assignments, exams, etc... for almost all courses... worth my time
@@dagkouta986 shut up
This gives new meaning to the song Smooth Operator by Sade
I studied quantum mechanics, from many different sources, But this is best one..... World's best!!!!! Thank you MIT And Dear Teacher.
The Hitchhiker's Guide to Quantum Mechanics.
Operator P42
Watching this a few times will eventually result a eureka moment of understanding not only how the Schrodinger equation works and can be derived, but also how it MUST be just so. It also takes the oft used term 'wave function collapse', and fleshes it out into how the measured observable (x, p or whatever) has to be an eigenvalue of the original wave equation, and it is modulated by an eigenfunction of the operator of choice.
This lecture is presented with all the skill of a masterful prosecutor building up an unassailable case brick by brick, culimating with the 'got you'coupe de grace of crowning the E scalar value with its operative symbol, thereby unlocking the gateway to quantum wave mechanics.
It is little wonder that the students give a warm round of applause at the end of this. But had they been able to fully digest the minutiae and nuances of this talk, it would have easily been a standing ovation. This is the quantum mechanics equivalent of the brilliant James Burke series of Connections from the BBC, or the equally as scholarly (but not quite so charismatic) Mechanical Universe presentations by David Goodstein from CIT.
+Ron Toolsie Did I get the last "genius coup" at the end (1:19:30)? Does putting a hat on top of E mean to "force" the energy to be quantized, to take only certain discrete values (the eigenvalues)? And (consequently) the other "observables" too? And if yes: isn't also the uncertainty principle hidden in this equation?It's an excellent lecture and Prof. Zweibach should indeed get standing ovations. I saved the video twice to be sure ... : )
Thanks for the recommendations, I'm going to watch both of those episodes!
at 1:00:10 them subtitles say 'Fourier told you you can't expand..." which is wrong (the professor didnt make that mistake, its only on subtitles); in fact Fourier 'told' us that we can expand any function as a linear combination of e^ikx.
MIT: where your substitute teacher just happens to be one of planet Earth's leading minds in String Theory
As a Peruvian, I feel proud of this genius!
I studied Quantum Mechanics more than 30 years ago - I wish I had had a lecturer like this one… 🙂
He is very funny at 49:0 when he goes on about how mathematicians struggle with the most simple case of commutation. He is right... you can get an entire lecture called "functional analysis" about that problem and it's quite ingenious.
I love this lecture! Very clear and funny.
Amazing lecture. Well structured, clear and extremely engaging; it takes you on a journey where your knowledge and understanding of the topic progressively grows, but it's so balanced that it doesn't force anything on you.
That is only halfway correct. The problem with non-relativistic QM is that it is not a proper physical theory, but that is usually not being explained to you while you are learning it. One should, for instance, tell the student that the Schroedinger equation does not conserve energy, momentum and angular momentum and that the projection operator formalism for measurement balances this out in just the right way to arrive at the correct physical results for the kinds of systems that can be described by non-relativistic theory to begin with. That entire background is usually missing from QM 101 lectures, including this one.
There is an error in the subtitles at 18:12 that repeats. Not direct delta but Dirac delta.
Thanks for your comment! It's fixed now. :)
MIT OpenCourseWare There is one more error at 52:02 . Not permission operators but hermitian operators.
As a matematician I beg to differ on what the professor said about us wanting to compute finite dimensional matrices. I think the most elegant mathematics is that of the infinite dimensional spaces that are behind this kind of phisics. I'm not at all scared by the fact that we are considering normed (or semi-normed) TVS and their duals without exhibiting any finite-dimensional basis for them, as long as I understand the underlying uniform structures and rigorously define what equality in the dual space means (i.e. weak equality on the test function space).
That's all cool, but you have to understand that physicists aren't giving a crap about any of that detail. For one thing we know that the SE is unphysical. It's a toy model that gets you exactly nowhere in real physics. For us the buck stops at the Dirac delta, which is the one line poor man's version of three hundred pages of functional analysis textbook. The stuff that we really care about (relativistic quantum field theory) is outside of the reach of serious mathematics for now as far as I know.
@@schmetterling4477 Oh, then I misunderstood what he was saying. I tought he meant "scary" as if we wouldn't want to deal with it, since I actually find it fascinating and that's why I'm all about it; but he probably meant it in the sense that we need to build a coherent theory which is sound and compelling, whereas for phisicists is more about the actual meaning of those quantities in their model.
@@giacomocasartelli5503 I also find functional analysis to be a fascinating mathematical discipline as it brings some sense of order into this infinite mess of functions. It just doesn't do much for physics because the problems with quantum mechanics do not stem from mathematical corner cases. They are deeply embedded in the core definitions of physics that all depend on a geometric substrate that we call "the physical vacuum". All our successes begin there, but so do all our failures. What needs to be exorcized is the notion of R^n as the underlying tangent space of reality. That's the end point and not the beginning, but for now we treat it as both and that's just wrong.
I love to watch this, I dont understand much but its great lecture
@12:09 I would have thought that the multiplication is the operator acting on a matrix and a vector. The latter one being the objects. Basically like this Mult(matrix, vector).
Excellent Lecture very clear.
I have been going crazy trying to understand operators but this video really helped.
Lies again? Laundry Operator
I love the hitchhiker's guide to the galaxy reference
Wonderful! It was updated to the high quality! Finally!
He's a brilliant lecturer. Absolutely brilliant.
1:03:11 here a is the Eigen value right?
And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
Never saw someone explain Eigenvectors as greatly before ! 27.00
Watch 3B1B's video
27:00 - now click it.
Beautiful blackboard hand writing to say the least of this professor, Awesome MIT Professorship!!
35:07 energy operator V(x hat) ???? 55:00 energy collapses to eigenfunction psi_a 57:30 1:03:00 ?????? 1:12:00 ...... this is the operator that realizes the energy
Watching Mr. Barton Zwiebach's elegant explanation of deriving iħ ∂ψ/∂t = H^ψ (TDSE) and H^ψ = Eψ (TISE) is like going back in time to the first quarter of the 20th century and meeting one of the greatest minds in QM (Heisenberg in 1925 and Schrödinger in 1926), both of whom revolutionized physics with such cognitive cataclysm!
Anybody who shows you a "derivation" of the Schroedinger equation is performing a parlor trick for you. It can't be properly derived from anything, if for no other reason than that it's completely wrong. At most one could argue that it's a non-relativistic perturbation solution for quantum field theory, but I am not sure it's even that (you can see this because it doesn't include the Pauli exclusion principle, for instance, which should not drop out in a proper perturbation theory).
As a mathematician who has worked with the Weyl algebra I found his comments about mathematicians amusing, and quite wrong. There are things that mathematicians find difficult to understand in quantum mechanics since it has not been made rigorous but the Heisenberg commutation relation is not one of them.
John Smith
I think he was just teasing mathematicians. Of course, mathematicians work with infinite dimensional spaces and hold seminars on operator theory all the time. If it weren't for mathematicians, physics wouldn't be where it is today.
He is just refering to the fact that the Heisenberg commutator requires the operators to be unbounded, the other one does not. This is what makes it more complicated.
Excellent explanation.
52:01, the subtitles got it wrong. He said "Hermitian operators" and not "permission operators".
Thanks for the note! The caption has been updated.
@@mitocw oh wow! Thanks for the speedy fix.
1:03:11 here a is the Eigen value right?
And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
I'm Interested in the DIAGAGNOLIZATION of matrix EIGENVECTORS, and VECTOR using Taylor expansion and DETERMINANT for infinite series and PAULI MATRIX and Clifford Algebra for solving the Schoringer Equation And HEINGBER uncertainty for QUANTUM FIELD PERBUTATION
A couple of SiFi stories have "pointed out" that the Universe is a point, ie the Temporal POV IS Singularity property, that is the Philosophers "indescribable" temporal superposition spin-spiral function cause-effect of time duration timing modulation, we are Totality embedded in.., but cannot describe because it's "No-thing", e-Pi-i omnidirectional-dimensional connection by Pi-bifurcation Exclusion Principle that "floats" numberness in macro-micro, divergence-convergent, Vanishing point-positioning, ..and is the pure-math Superspin-spiral pivot of here-now-forever localization circularity.., the Condensed Matter and Theoretical Quantum-fields Mechanism of AM-FM In-form-ation substantiation that is the subject of the lecture. (By default?)
If the lecture starts as it should with "known physical empirical laws" then this is the hierarchical dominance of phase-locked coherence-cohesion probabilistic pure relative motion logarithmic pulse-evolution differentiates in potential mathematical motion, possibility.., an Equation of this particular Timing-spacing integration wave-particle coordination-identification.
By default, the Quantum Operator Fields Modulation Positioning Computation Mechanism is the only Actuality, in projection-drawing Perspective, Principle.
The build-up at the end is excellent! One question remains. He stated that Schrӧdinger Wave Equation is "deterministic." I cam cautious about accepting that but I would like to hear more about how it is deterministic.
it's deterministically probabilistic :) lol
More often than not, you'll get a range of answers but only that range of answers. It's deterministic in that sense.
Mace Right, in other words, the probabilities are deterministic in the sense that waves on an ocean affect other waves in a certain pattern?
The wave equation has no physical meaning. It's only when you calculate the probability function that you get real world implications. The wave equation will give you this probability function exactly. But, yeah, the probability function will never give you an exact answer as to the properties of a particle at a certain time.
That is what I'm to understand anyway...
CrushOfSiel OK, but the wave equation describes the mathematics of momentum of the photon while the particle is the math of position. What it "really" is there is no one answer at this point.
there is also another version of 8.04 taught by Allan Adams, you guys can try him if you don't understand barton zwiebach
Do you have the link? I can't find it.
@@ながれる季節 yes sure
ruclips.net/p/PLyQSN7X0ro21XsVfRHhiWGEEJigdjpF3s
I don't get why there's two energy operators, the short one @1:15:39 and two term one @1:20:20 ? In what context can each be used?
The description got the professor's name wrong. He is Prof. Zwiebach, not Prof. Zweibach!
Nice catch! You are the first person to notice and mention it in 6 years!! We've updated the descriptions (Lecture 8 was also wrong).
Uncertainty of the random variable "operator" is equal to its standard deviation (38:35)
1:01:42 watch with pause and subtitles
I think the student meant his question about the delta function being an operator in a different way. Hes asked himself whether it even makes sense to multiply anything f with the delta function.
Yes, one can multiply smooth test functions with the delta function just fine. The mathematical difficulties that arise in non-relativistic quantum mechanics are only pathological from an exact math perspective. They are not actual physical problems. It gets much, much worse in relativist quantum field theory where divergences are NOT caused by poor use of mathematics. They are the results of real physical phenomena and they have to be dealt with accordingly by using proper physical intuition about why they arise and how one can still extract useful phenomenological results from the formalism despite them.
@45:50, why x and p order matters means that when you measure one you have difficulties measuring the other?
If you could measure them both like you would classically, then it shouldn't matter in which order you measure them.
Around 34:09 he shows that V(x hat) Psi(x) = V(x) Psi(x)
I don't follow his argument / proof. Any help?
***** Thanks for the reply. It helped!
+David Gillooly Watch Lecture 4 again. Prof Adams demonstrates this operator there, and tells us how it works.
+David Gillooly It's a hermitian operator for a measurable in position x^hat, and it operates on the function to give you the position eigenvalue of the function. Kind of like having a continuity of infinitesimal kets and the operator gives you the eigenvalue of the ket. You can do that with most Potential functions as a measurable, this can be proven through taylor expansion as it acts on each variable.
5:48: "This operator acts to roughly give you the momentum of the particle."
except, that, as we all know, ih*psi ' = E*psi. It DNE p*psi, and never has. I am confused why he thinks that.
Just answered my own question:
When psi is taken as a derivative of time, then ihΨ ' = E*Ψ.
When psi is taken as a derivative of displacement, then ihΨ ' = p*Ψ....
So much thanks for this MIT team, i love physics but my professors just cant explain it!
i love the "professor kidnapped by pirates" subplot
Isnt there a mistake at 35:35 ? Should be ... + x*v(x)*psi(x), no? (the x is missing)
Same here i also thought about that but i think v(x) is one operator therefore it is v(x) . Psi(x) bot i do not know 100% if you find it let me know
Brilliantly given lecture, was really drawn in.
1:08:30 - I do have to say I disapprove of things just being "handed down from on high" to be taken on faith. Last lecture we got handed the momentum operator, and this lecture we're getting handed Schrodinger's equation. That's not really "teaching" - that's just training technicians. On the other hand, I stumbled across this paper a couple of days ago:
www.researchgate.net/publication/328332637_How_to_Un-_Quantum_Mechanics
It's simply AMAZING how thoroughly the writer derives so much physics from such a meager starting point. I'm still pouring over it, gradually absorbing more and more content.
Thanks!
At 52:08, it is Hermition operators, not "permission".
Thanks a lot . I have a question : there are 2 energy operators !! One is the summation of the momentum and the potential operators , and the other is the one contains the partial time derivative !! Why :/ ?! I'm confused .
Ben Sama The first is the time-independent Schrodinger equation, which just calculates the energy eigenvalues of the eigenstates; the system as a whole is time-invariant and states don't evolve with time(stationary states). The second is the time-dependent Schrodinger equation which shows the time evolution of the states of a wavefunction when you don't measure a system to make it undergo collapse.
at 2:20 I think it should be P(dx) = |Phi(x)|^2 *dx, since P(x)dx would be 0.
No, P(dx) would be meaningless. P(x) is the probability density at the point x - an ordinary function of x. The integral of P(x)dx over all x must = 1.
Best things of the universe are always hidden. They are not put up on advertisements boards or tv commercials. They are always discovered by keeping a meticulous perseverance. "Truth is not for all men but only for those who seek."- Ayn Rand
Thank you Universe!
1:09:20 shrödinger eq
The moment he said "I'm not gonna do that" I was immediately aware that this will be a tough ride :)
Using the operator P42 ---> 42. Is this a reference to "The Hitchhikers Guide to The Universe" I wonder?
Very very good lecture. All the previous lectures was like isolat islands and focused to "draw attention to me I am hero" even the pirate theater target to the same. I think the fifth lecture by this gentlemen "great teacher" covered all the previous artistic plays. I think MIT may make a survey from different level of educated people like, those who know QM, familiar with QM or don´t know, to use the donated money on real lectures.
Unity-connection inclusion is operational Actuality, self-defining aspects of real-time Infinity as abstract Operators that specify a particular aspect positioning in Logarithmic spin-spiral Timing-spacing coordination, Fluxion-Integral Temporal superposition Calculus, and Qbyte line-of-sight identification of relative-timing density-intensity ratio-rates.
Forward-Reverse lead-lag pastfuture potential now-> sync-duration, an abstract process of POV identification, is complex completion of vertices in vortices nodal-vibrational transverse trancendental condensation. This is the inside-outside orientation of Intuition required by Actual Intelligence before a student should attempt to rediscover a topic attributed to an application with personalised names. (Just saying)
Fractal conic-cyclonic Superspin-spiral Superposition Totality Correspondence in time-timing Reciproction-recirculation Singularity positioning.., this is the inside-outside presence of holography, functional e-Pi-i Apature Observation.
1:03:11 here a is the Eigen value right?
And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
Thank you Professeur Dalek
good lecture, i'm a bit confused about there being 2 energy operators though...any insight?
As schroedinger`s eq tells us they are equal, it is basically the same operator in different forms.. Kind of like 1+4 and 2+3 is the same number.
What a beautiful lecture.
Merci beaucoup MIT
Drrrr this is so obvious X(f) is the function of the vector it's super clear, yeah I didn't whent to school but I find it fascinating
8:31 why is expected value of p depended on the conjugate of wafefunction, shouldn’t it just be based on the wave function itself
The expected value of p is based on the _square_ of the wavefunction, but since that is a complex function, to square it you multiply it by it's complex conjugate.
17:42 An MIT open course about Schrӧdinger Equation, I expected to get close to the universe's secret. But not that close... (I see what you did there)
This guy is actually even better than the other dude
I went to a Community College and my professor was at least as good as this guy. My professor received his PhD from the University of Chicago. So, you don't need to attend an expensive university to get a great education. It's what YOU put into it.
Barton is doing this lecture because Allan is in the hospital after an unexpected pirate attack
1:08:20 - Yes, you CAN derive Newton's equation F=ma, using the principle of least action. It's standard fare in classical mechanics texts.
That's what he refers to when he says you can derive Schrodinger's equation using unitary evolution (or if you want to be picky the Feynman path integral is the formulation in QM of the principal of least action), but you can't prove unitary evolution you just take it as postulate. Just like you don't prove the principle of least action, you just take it as your starting point.
finally someone actually like to teach
This was amazing lecture takes quantam mechanics to different dimension I can feel Prof Adams downcast on not able to introduce schorimder equation in it's full glory
1:03:11 here a is the Eigen value right?
And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?
Can anyone please explain why we substitute f(x) with unit operator at 45:21 ?
p and x can be thought of as matrices and the outcome of those has to be a matrix aswell
@@bobfake3831 Thank you for explaining, now it has started to make sense.
In the last video a guess was made that =∫lΨ(x) l^2·p(x)·dx. In this video, p(x) has been cleverly replaced, but lΨ(x) l^2 has also been changed to Ψ*(x). Does anyone know why? As far as I see it a complex number times it conjugate would give us lΨ(x) l^2, når just the conjugate alone.
still helpfull all these years later!
I have one problem. Think about position, for example, everytime we measure an object, we get the same result. If the result that we measured is eigenvalue, why we always get the same result? (Does that mean that eigenvalue is unique?)
After the wave function collapses to a value a, you end up with AΨ = aΨ, in other words, after the wave function collapses, the measured value becomes the only eigenvalue. Any other eigenvalues before the collapse are now gone
I traveled in a timelike Geodesic, bent time, and got here super quick.
Very good explanation for an ordinary man a boon lecture thanks a lot for the professor.
Momentum is such a mystical term. How does a massless photon have momentum. Is it only velocity we are talking about?
Momentum being defined as mv only works for things with mass (and non relativistic speeds). Einsteins equation gives insight to this with E² = (mc²)² + (pc)². Setting m = 0 and solving for p, we get p = E/c = (hυ)/c = (h*(c/λ))/c = h/λ
Could someone explain why there is an V(x)?
p^2/2m generally represents the kinetic energy of the moving mass. V(x) is potential energy on point x.
+Abdurrezzak EFE Thanks! :)
SE... You can tell the energy where it's at ( located )....
Why is there the conjugate of the wave function in the beginning ? For p
I did calculation on average value of momentum from equation at 8:15 , it comes to be infinity!! Why??? please help
How can you calculate a integral if you don't know the functions (psi) involved?
I +bonnome2 wave function times conjugate of wavefunction is 1 if its normalised, if not it's just some finite number, nothing to do with integral.
Yeah but you need to do the operator on the wave function. According to what is on the blackboard you would get ∫hk dx = hkx from infinity to zero infinity. This is undetermined.
bonnome2 I do applied operator on wave function, for example e^ikx, then also I am getting p mean, infinity. I AM REALLY CONFUSED 😕
bonnome2 how it's undetermined? Answer is infinity
Very clear and interesting thank you.
At 8:27: “The thing that we want to do now, is make this more general.”
Me: “Oh no… Now it comes… And we’re only at the beginning of the lecture…”
this helped me to put my ideas in order thanks for share
1 or unity concept of existence, the elemental principle of Logarithmic Time Communication and dominant floating prime point in even symmetricali-reflection of log base 2, square identity via the functional integration-differentiation operation of "e", the Inflation +/- zero-infinity distribution in which Pi bifurcation, fractalisation is Quantum-fields Mechanism Singularity positioning, holographic quantisation of implied potential pure relative motion and Algebraic Calculus of continuous metastable proportioning probability in creation connection. => e-Pi-i QM In-form-ation substantiation Operator.
From Observation/Philosophy: "It's all ways Now", "All IS vibration", "Everything is connected" @.dt Absolute Zero Kelvin i-reflection containment phase-locked "mathematical" statements => real-time/sync of pure relative motion, formulae.
(Thanks to the student who mentioned Dirac Delta Function, I have another conceptual equivalent to the idea of the cross-section of a string/axis in unit connection coordinates.)