I am a PhD Mathematician with a specialty in differential algebra: the study of how to solve all sorts of nonlinear FPDEs = functional PDEs. Recently, I tried to solve the S-equation for a Lennard-Jones potential. I then realized that the reason I cannot solve is that it is impossible to solve over an INFINITE spatial domain: -infinity < x < infinity. Psi would have to decay fast enough at both ends in order for the integral of Psi*Psi-bar over all real x to be FINITE let alone 1.
Yes, I have a masters in physics, and we put as many constrains as we can in order to solve this, even for numerical solutions other way, we would get no results
@@soyoltoi Well, it seems to be the only methods right now for figuring out what classes of solutions exist for linear differential equations. e.g. rational solutions, or rational functions with exponentials adjoined.
Interesting. Even the simple model of the Helium atom you describe is essentially a sort of 3 body problem... 2 electrons, and one massive nucleus. And we know that that is difficult enough to solve even classically, let alone with the quantum complications.
Nice video! I did my PhD on solving this equation for multi-electron systems. You can’t solve them analytically, but fortunately they’re pretty easy (that’s very relative) to solve numerically. There are some much scarier beasts out there, like non-linear equations or the Dirac equation, for which it’s even difficult to build an exact Hamiltonian if tou have more than one electron.
I cannot agree with your statement that atoms "are pretty easy to solve numerically". Sure, their electronic structure is simpler than molecules' (because of the spherical symmetry and lesser importance of dynamic correlation) but it's still a superexponentially scaling problem. And of course it's also a matter of desired accuracy. Getting, say, 10% accuracy on energy levels is relatively easy (Hartree-Fock) but calculations of high accuracy (say, energy levels to 1 cm-1 accuracy) are impossible apart from the very lightest atoms.
@@luckyluckydog123 I never said the SE is easier to solve for atoms than molecules. I said it’s relatively easy to solve it for multi-electron systems, when compared to other equations out there.
@@AmokBR > I never said the SE is easier to solve for atoms than molecules I never said you said that. However, that's a true statement. Do you not agree? Also, saying 'it's relatively easy because the Dirac equation is harder" is borderline sophistry, because it suggests that accurately solving the SE for atoms can be done at all (while in fact it is impossible to solve for the energy levels to an accuracy comparable to the experimental one when Z>~4).
Cool video! I’ve heard for years about how we have a good solution for hydrogen but helium, let alone higher, was a whole other matter. Nice to have it confirmed and explained!
Very much enjoyed this, thanks. The richness of the solutions of the Schrodinger equations and its difficulty in solving reminds of the Navier Stokes equations with only a handful of analytical solutions yet such great complex behaviour.
Man this channel is golden, everything is explained so clearly. It's so interesting that people have even managed to discover how to calculate things of this nature.
I'd expect the |phi|^2 to be always smaller than a |phi| (if it were completely real for all values of x, like you show). It being normalized to 1, all values of it must be < 1, and hence the square of it would be smaller than itself, instead of larger.
A (real-valued) wavefunction being normalised to one does not imply that all values must be smaller than one. For instance, a normalised wavefunction with support in an interval of length less than one must have some values larger than one.
@@anonymizationoverload9831 You are correct that the video uses ψ rather than φ and furthermore it is the case that ψ (or Ψ) is in some sense the "standard" symbol for a wavefunction. That said, the reason isn't because of the other fact that φ is used to denote the golden ratio in mathematics. Indeed, φ is also an extremely common symbol for wavefunctions and is usually the next in line for a wavefunction in the context where ψ has already been used to refer to a different wavefunction. Those two facts aren't really related to one another in any sense, it's not as if letters are restricted to only one single use in any context-after all, we don't have that many to pick from in total, at least relative to the number of mathematical objects they need to denote. Another example of a common use for the symbol φ would be in spherical coordinates where, depending on if you ask a mathematician or a physicist, it denotes the polar or azimuthal angle respectively; or cylindrical coordinates where it denotes the azimuthal angle. Since it is commonly used as an angle like this, another similar use which is extremely common is using φ to denote a phase shift. Furthmore, Φ is commonly used to denote magnetic flux in physics.
So, how then it's useful if we almost can't solve it? Greate video I hope you continue simplifying the math of quantum physics " as physicists doing it" big thanks.
I was thinking about how quarks are attracted to each other but also repel in a way so they hold a formation in some manner. (It reminds me of a L2 Lagrange point of a orbiting set of multiple body's in space. )
02:30 f: _The kinetic energy plus the potential energy gives us the total energy._ Actually, the usually biggest part is missing here: The rest energy.
Wish I could find a video with the next step - "Let's solve it numerically!" and lays out how to attack it, picks an open solver, and lets their desktop computer crunch out the answer. How big of an atom or molecule could a modern desktop and GPU solve in, say, a weekend?
I have an equation shows how information about Schrödinger solutions for an atom’s electron in a gravitational mass is conserved by the surface area entropy as the gravitational mass collapses to being a Schwarzchild mass. If anyone wants to see it there is a full video on my channel.
If it is not possible to solve the Schrodinger Eqn. of complex atoms, how do we construct the modern model of the atom? (I mean, those s and p's and d orbitals and their quantum numbers etc.)
You use simplified approximations that are more solvable, like considering only one of the electrons at a time while treating the rest of the electrons as a fixed density of charge (Density Field Theory)
They make approximations based on assumptions that allow them to simplify the equations. They can also use numerical methods to compute results with better and better accuracy at the cost of not getting an exact answer.
That's a misinterpretation of Neutrino charges. The Gluon "cloud" is equivalent to the mass they are intrinsically balanced forces but the actual energy is the particles' temperature, the gluon is a reflection of that compression. So the Statement should be ... "chiral symmetry equivalent to 99% of proton's or neutron's mass"
Not a physics major, but I'm guessing from the gradient symbol that those equations are PDEs which makes sense why they are impossible. I remember from me watching a lectures from MathTheBeautiful explaining them for my diff equations 2 class specifically when he introduced them. ODEs which we were used to are pretty much solvable (at least numerically most people have given up finding analytical solutions) PDEs however you don't even know how to begin to solve it numerically and worse the entire problem could change by adding a term or changing a sign changing it to a fundamentally different problem. There are people who dedicate their career to figure out how to numerically solve a specific type of PDEs
Numerically solving PDEs are fairly well studied tbh. There are methods like crank nicolson and implicit method which can always give you a converged solution. Once a proper boundary condition is found, everything after that can be algorithmically solved.
In what sense does the Schrödinger equation tell the evolution over time? It tells how the wave function changes over time, in terms of partial derivatives. But it doesn't tell how a quantum jump evolves. An isolated atom stays in a stationary state until it jumps to a lower energy stationary state. The Schrödinger equation doesn't tell about that. We have practically no idea of how a quantum jump evolves.
We have a huge advantage compared to Schrödinger etc during the 30:s, in that we can use computers to solve, at least numerically, equations like that.
What really would happen in experiment? *Much in the past, it was believed that electricity and magnetism were distinct and independent. But, James Clerk Maxwell, a Scottish🇬🇧 mathematician showed that they are one and United them into electromagnetism. Now, let's have a scenario where there are two different things that each follow electricity and magnetism respectively, and we bring in another thing that actually follows the electromagnetism principle, and apply it to both...then, what would happen to those things? What effect would it have on them??*
And, we differential algebraists classify the S-equation as an "easy" equation to solve because it is still a LINEAR PDE. We haven't even gotten to NONlinear versions of it, which exist in my Handbooks of PDEs by Soviet authors Polyanin & Zaitsev.
The gradient of the probability wave of the electron looks like an expected electron velocity in space and time. So, an orbital with higher spatial frequency can hold an electron having more average kinetic energy in a stationary state.
With a clean-shaven look the new video is also very clean,simple , and good. Start perturbation theory Feynman diagram,relativistic theories,invaiance & types,etcetera...
This video is missing one important thing, what each symbol mean in this equation. As far I understand first Psi is `(R^2, R)->C` aka (electron position, time) to complex number, second is `(R^2, R^2, R)->C` (first electron position, second electron position, time) to complex number, this mean you do not only add some terms to equation but change type of function too.
Er, if ψ must sum to 1, then its magnitude must everywhere be less than 1. If ψ is less than 1, then ψ squared is less than ψ. Your graph shows |ψ|2 as > ψ.
Very informative and explained in a fairly approachable way. Take a word of a musician :) My great teacher of physics once told us in the classroom that unless some particular physical theory is usable in any meaningful way, it doesn't really matter. This video reminded me of his words. Should I ask then a rhetoric question if Shrodinger's equation has any techincal applications... obviously not. Best regards, very interesting channel. As obscure as it all looks to me, at the same time those tiny glimpses of understanding seem to hint at a completely different yet amazing alternate reality :))
QM classicalized in 2010: Juliana Mortenson website Forgotten Physics uncovers the ‘hidden variables ‘ and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie,Planck,Bohr etc. A proton is a collection of @1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. So,no. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon.
What do you think about 2022 nobel prize for Bell's inequalities and denial of "quantum entanglement" process? Does that mean Einstein denial for this process is true?
Is the other way around, the experiments done by the new noble prize winners prove quantum entanglement is legit, and discards the "hidden variables" explanation, so Einstein was wrong about that.
Given my masters was in numerical analysis/DE methods, I don't find the idea that there is no analytic (pen & paper) solution very illumintaing (that it's hard/impossible to get analytic solutions for DE is something of truism, has nothing to do with QM really), yes, computers are essential. Sorry don't mean to troll.
Be nice to see it applied to a single pair of electron_positron/s caught in balance by charge in a long-term death spiral, and upon decay emit the energy-of-annihilation. Sternglass-Einstein found a named meson of two, counter-rotating pairs in the lab by their dynamic property equations, 1950s. It would be interesting to see what the Schrodinger result will be ! Fun stuff 🍺
And here I am grade 7 we currently studying Speed and Acceleration but it's so boring and easy so I tried to solve Schrodinger equation time independent form first and I still can't get the half of it I get lose on the Sine because I'm not really so familiar in it but I get all the psi and constant
*Atomic orbitals not useful for large atoms* Perhaps this is why electronic configuration is not a very good tool since all electrons (1s2 2s2 ... 7p6) are assumed to be spinning around a proton instead of Og or other nucleus and why ? Because Schrodinger equation is impossible to solve as soon as a nucleus is more than just a single proton. *Sigh*
This video is incorrect. The Helium ground state wavefunction can be easily solved with pen and paper, no computers, using a series of variational ansatzes, and this is historically how the then-new quantum mechanics was verified. It's not even all that difficult, because the phase space is 3 dimensional. The first excited state is doable also.
this comment is imprecise. The pen-and-paper solutions to the helium wave functions are only crude approximations. Also, the phase space is not 3 dimensional (and in any case in quantum mechanics it is not generally convenient to work in phase space). The dimensionality of phase space is 6*N_of_bodies so the helium atom it's 18-dimensional (full problem) or 12-dimensional (clamped nucleus approximation).
@@luckyluckydog123 The wavefunction space after rotational reduction is three dimensional, and the variational solutions are not 'crude approximations', they are within 1% of the exact solution in the region of significant wavefunction variation even with pen and paper. Wavefunctions aren't over phase space, (which is 12 dimensional not 18 dimensional BTW, center of mass doesn't count) but over configuration space, which is 6 dimensional. Three of those dimensions are determined by rotational invariance, so the wavefunction you need to do variations on is in the three remaining dimensions. The functional form is restricted by the one-particle solution to be exponentially tailing off at large x, and a Pade-style rational function in the exponent gets you the rest of the variational wavefunction. It was done before computers in the 1930s getting Helium energies to better than 1% accuracy.
Please never spell Schrödinger like that. If you can't find the ö character in your keyboard or compose it with umlaut (double overdot) and o, do what German speakers do: spell it Schroedinger. But never Schrodinger. Respect for the famous physicist's name.
I am a PhD Mathematician with a specialty in differential algebra: the study of how to solve all sorts of nonlinear FPDEs = functional PDEs. Recently, I tried to solve the S-equation for a Lennard-Jones potential. I then realized that the reason I cannot solve is that it is impossible to solve over an INFINITE spatial domain: -infinity < x < infinity. Psi would have to decay fast enough at both ends in order for the integral of Psi*Psi-bar over all real x to be FINITE let alone 1.
Yes, I have a masters in physics, and we put as many constrains as we can in order to solve this, even for numerical solutions other way, we would get no results
ok
@rey louis you can get all that knowledge! Study maths and get math books, nobody is born with knowledge like that
How useful is differential Galois theory in your opinion?
@@soyoltoi Well, it seems to be the only methods right now for figuring out what classes of solutions exist for linear differential equations. e.g. rational solutions, or rational functions with exponentials adjoined.
I remember our Quantum Physics lecturer solving this for Hydrogen. It took the whole hour.
Interesting. Even the simple model of the Helium atom you describe is essentially a sort of 3 body problem... 2 electrons, and one massive nucleus. And we know that that is difficult enough to solve even classically, let alone with the quantum complications.
Nice video! I did my PhD on solving this equation for multi-electron systems. You can’t solve them analytically, but fortunately they’re pretty easy (that’s very relative) to solve numerically.
There are some much scarier beasts out there, like non-linear equations or the Dirac equation, for which it’s even difficult to build an exact Hamiltonian if tou have more than one electron.
yikes. non-linear + dirac term + PDE, with an exact hamiltonian for an entangled system...NASA, where's your supercomputer?
I cannot agree with your statement that atoms "are pretty easy to solve numerically". Sure, their electronic structure is simpler than molecules' (because of the spherical symmetry and lesser importance of dynamic correlation) but it's still a superexponentially scaling problem. And of course it's also a matter of desired accuracy. Getting, say, 10% accuracy on energy levels is relatively easy (Hartree-Fock) but calculations of high accuracy (say, energy levels to 1 cm-1 accuracy) are impossible apart from the very lightest atoms.
@@luckyluckydog123 I never said the SE is easier to solve for atoms than molecules. I said it’s relatively easy to solve it for multi-electron systems, when compared to other equations out there.
@@AmokBR > I never said the SE is easier to solve for atoms than molecules
I never said you said that. However, that's a true statement. Do you not agree?
Also, saying 'it's relatively easy because the Dirac equation is harder" is borderline sophistry, because it suggests that accurately solving the SE for atoms can be done at all (while in fact it is impossible to solve for the energy levels to an accuracy comparable to the experimental one when Z>~4).
@@luckyluckydog123 Sure, whatever you say.
For a moment I thought it was another channel on Physics.
😅👍
@ms0:seplugins due to new look of sir....
Yeah, I like the new look though.
This was a thoroughly informative and accessible walkthrough. Thanks!
Cool video! I’ve heard for years about how we have a good solution for hydrogen but helium, let alone higher, was a whole other matter. Nice to have it confirmed and explained!
Very much enjoyed this, thanks. The richness of the solutions of the Schrodinger equations and its difficulty in solving reminds of the Navier Stokes equations with only a handful of analytical solutions yet such great complex behaviour.
Your videos have some of the best explaination about physics. They really are gold.
Omg BRO
You are look like a PROFESSOR.😮👍🏻👍🏻
Man this channel is golden, everything is explained so clearly. It's so interesting that people have even managed to discover how to calculate things of this nature.
You have a real knack for explaining difficult subject matter.
I'd expect the |phi|^2 to be always smaller than a |phi| (if it were completely real for all values of x, like you show). It being normalized to 1, all values of it must be < 1, and hence the square of it would be smaller than itself, instead of larger.
I'm pretty sure it's psi, not phi? Phi is (in math at least, not sure about physics) the golden ratio
A (real-valued) wavefunction being normalised to one does not imply that all values must be smaller than one. For instance, a normalised wavefunction with support in an interval of length less than one must have some values larger than one.
@@anonymizationoverload9831 You are correct that the video uses ψ rather than φ and furthermore it is the case that ψ (or Ψ) is in some sense the "standard" symbol for a wavefunction. That said, the reason isn't because of the other fact that φ is used to denote the golden ratio in mathematics. Indeed, φ is also an extremely common symbol for wavefunctions and is usually the next in line for a wavefunction in the context where ψ has already been used to refer to a different wavefunction. Those two facts aren't really related to one another in any sense, it's not as if letters are restricted to only one single use in any context-after all, we don't have that many to pick from in total, at least relative to the number of mathematical objects they need to denote. Another example of a common use for the symbol φ would be in spherical coordinates where, depending on if you ask a mathematician or a physicist, it denotes the polar or azimuthal angle respectively; or cylindrical coordinates where it denotes the azimuthal angle. Since it is commonly used as an angle like this, another similar use which is extremely common is using φ to denote a phase shift. Furthmore, Φ is commonly used to denote magnetic flux in physics.
So, how then it's useful if we almost can't solve it? Greate video I hope you continue simplifying the math of quantum physics " as physicists doing it" big thanks.
I was thinking about how quarks are attracted to each other but also repel in a way so they hold a formation in some manner. (It reminds me of a L2 Lagrange point of a orbiting set of multiple body's in space. )
02:30 f: _The kinetic energy plus the potential energy gives us the total energy._
Actually, the usually biggest part is missing here: The rest energy.
What program you use to make video, can you share little
Nice new look bro 🔥
Great defining Parth. Keep enjoying it and make rocking to others too and to have fun with it.
Great video. Glad to see you again.
Wish I could find a video with the next step - "Let's solve it numerically!" and lays out how to attack it, picks an open solver, and lets their desktop computer crunch out the answer. How big of an atom or molecule could a modern desktop and GPU solve in, say, a weekend?
Hey there can you provide some detailed stuff for harmonic oscillators, thank you in advance Mr. Parth G
I have an equation shows how information about Schrödinger solutions for an atom’s electron in a gravitational mass is conserved by the surface area entropy as the gravitational mass collapses to being a Schwarzchild mass. If anyone wants to see it there is a full video on my channel.
Wow! I understand the equation more better than before.
Thank you sir
Delete "more"!
Thanks for the video, well made and very interesting!
Schrodinger be like
I know it tough but it works
If it is not possible to solve the Schrodinger Eqn. of complex atoms, how do we construct the modern model of the atom? (I mean, those s and p's and d orbitals and their quantum numbers etc.)
You use simplified approximations that are more solvable, like considering only one of the electrons at a time while treating the rest of the electrons as a fixed density of charge (Density Field Theory)
They make approximations based on assumptions that allow them to simplify the equations. They can also use numerical methods to compute results with better and better accuracy at the cost of not getting an exact answer.
I was expecting to see how the wave function for the helium atom looks like at the end, but cool video nonetheless.
Sorry I couldn't get anything from this video, distracted by your new style! XD
Jokes aside, thanks for the good explanation! Great work!
Can u explain how chiral symmetry breaking from the gluon cloud interactions is responsible for 99% of proton's or neutron's mass?
That's a misinterpretation of Neutrino charges. The Gluon "cloud" is equivalent to the mass they are intrinsically balanced forces but the actual energy is the particles' temperature, the gluon is a reflection of that compression.
So the Statement should be ...
"chiral symmetry equivalent to 99% of proton's or neutron's mass"
To account for everything, should we also calculate gravity, strong and weak forces?
new look is 🔥
also great vid as always
Bro your new look is 🔥. Also the video 🔥
Duuude new. Professor Schrodinger look. 👍
fantastic explanation
Not a physics major, but I'm guessing from the gradient symbol that those equations are PDEs which makes sense why they are impossible. I remember from me watching a lectures from MathTheBeautiful explaining them for my diff equations 2 class specifically when he introduced them.
ODEs which we were used to are pretty much solvable (at least numerically most people have given up finding analytical solutions)
PDEs however you don't even know how to begin to solve it numerically and worse the entire problem could change by adding a term or changing a sign changing it to a fundamentally different problem. There are people who dedicate their career to figure out how to numerically solve a specific type of PDEs
Numerically solving PDEs are fairly well studied tbh. There are methods like crank nicolson and implicit method which can always give you a converged solution. Once a proper boundary condition is found, everything after that can be algorithmically solved.
How to become a physicist and what we have to do after being a physicist🙏🏻
Please make a video on this🙏🏻
❣️I really love physics and universe
Oooo, who's this hansome young man! Looking sharp.
Great video once again. :))
In what sense does the Schrödinger equation tell the evolution over time? It tells how the wave function changes over time, in terms of partial derivatives. But it doesn't tell how a quantum jump evolves. An isolated atom stays in a stationary state until it jumps to a lower energy stationary state. The Schrödinger equation doesn't tell about that. We have practically no idea of how a quantum jump evolves.
That was excellent!
We have a huge advantage compared to Schrödinger etc during the 30:s, in that we can use computers to solve, at least numerically, equations like that.
What really would happen in experiment?
*Much in the past, it was believed that electricity and magnetism were distinct and independent. But, James Clerk Maxwell, a Scottish🇬🇧 mathematician showed that they are one and United them into electromagnetism. Now, let's have a scenario where there are two different things that each follow electricity and magnetism respectively, and we bring in another thing that actually follows the electromagnetism principle, and apply it to both...then, what would happen to those things? What effect would it have on them??*
Do you mean solving in closed form or numerically?
Great explanation.
And, we differential algebraists classify the S-equation as an "easy" equation to solve because it is still a LINEAR PDE.
We haven't even gotten to NONlinear versions of it, which exist in my Handbooks of PDEs by Soviet authors Polyanin & Zaitsev.
Thank you a thousand times
Excellent thank you.
The gradient of the probability wave of the electron looks like an expected electron velocity in space and time. So, an orbital with higher spatial frequency can hold an electron having more average kinetic energy in a stationary state.
Higher spatial frequency implies more nodes in the orbital, radial nodes and angular nodes. The ground state should have no nodes.
You are such a legend holy sh*t KEEP IT UP DUDE
With a clean-shaven look the new video is also very clean,simple , and good.
Start perturbation theory Feynman diagram,relativistic theories,invaiance & types,etcetera...
This video is missing one important thing, what each symbol mean in this equation. As far I understand first Psi is `(R^2, R)->C` aka (electron position, time) to complex number, second is `(R^2, R^2, R)->C` (first electron position, second electron position, time) to complex number, this mean you do not only add some terms to equation but change type of function too.
Er, if ψ must sum to 1, then its magnitude must everywhere be less than 1. If ψ is less than 1, then ψ squared is less than ψ. Your graph shows |ψ|2 as > ψ.
looking sharp! i like the moustache (and, of course, the fun physics content) :)
Hi parth can you made video on explaining superfluids with there properties.
Say you did solve this equation for the helium atom, how does one confirm their solution is correct and agrees with nature?
Very informative and explained in a fairly approachable way. Take a word of a musician :)
My great teacher of physics once told us in the classroom that unless some particular physical theory is usable in any meaningful way, it doesn't really matter. This video reminded me of his words. Should I ask then a rhetoric question if Shrodinger's equation has any techincal applications... obviously not.
Best regards, very interesting channel. As obscure as it all looks to me, at the same time those tiny glimpses of understanding seem to hint at a completely different yet amazing alternate reality :))
Settle to lower energy..rotate around higher energy
Sir
Large scale object have quantam effect ?
Wathing from IOK ..love you
QM classicalized in 2010: Juliana Mortenson website Forgotten Physics uncovers the ‘hidden variables ‘ and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie,Planck,Bohr etc. A proton is a collection of @1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. So,no. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon.
Sir how to contact you?
Who is this clean cut guy? And what happened to Parth?
I forget to say exelent explanation..
serch helium chemical reaction, nucleas is what reli mathers, posetive charges is give electrone probabylity
So, whats the solution?
Wait, I thought the Lagrangian was potential energy plus kinetic energy. What's the difference?
What do you think about 2022 nobel prize for Bell's inequalities and denial of "quantum entanglement" process? Does that mean Einstein denial for this process is true?
Is the other way around, the experiments done by the new noble prize winners prove quantum entanglement is legit, and discards the "hidden variables" explanation, so Einstein was wrong about that.
The Schrodinger Equation seems to be impossible to PRONOUNCE, too! "schro" is pronounced to rhyme with FUR (not to rhyme with SHOW).
Fantastic!
Given my masters was in numerical analysis/DE methods, I don't find the idea that there is no analytic (pen & paper) solution very illumintaing (that it's hard/impossible to get analytic solutions for DE is something of truism, has nothing to do with QM really), yes, computers are essential. Sorry don't mean to troll.
Beautiful 🖤
Why isn't the Dirac equation more famous? Schrodinger:s equation is not relativistic, while Dirac's Dirac equation is.
Be nice to see it applied to a single pair of electron_positron/s caught in balance by charge in a long-term death spiral, and upon decay emit the energy-of-annihilation.
Sternglass-Einstein found a named meson of two, counter-rotating pairs in the lab by their dynamic property equations, 1950s.
It would be interesting to see what the Schrodinger result will be !
Fun stuff 🍺
I keep getting drawn to that thing on your upper lip.
"The last time I saw something like that, the whole herd had to be destroyed!" - Eric Morecambe
And here I am grade 7 we currently studying Speed and Acceleration but it's so boring and easy so I tried to solve Schrodinger equation time independent form first and I still can't get the half of it I get lose on the Sine because I'm not really so familiar in it but I get all the psi and constant
Nice stache g
If we introduce a feline particle, would we then have a purrfect solution ? (On my way out ! )
Quick mention, the reflection on your glasses is already distracting me, yep, look three times while writing... lol.
Woo you tried to solve the sc equation but reached to solve the hair style. 👨🏫
Wtf have you done with that amazing hair bro
What are the chances I would comment?❤
*Atomic orbitals not useful for large atoms*
Perhaps this is why electronic configuration is not a very good tool since all electrons (1s2 2s2 ... 7p6) are assumed to be spinning around a proton instead of Og or other nucleus and why ? Because Schrodinger equation is impossible to solve as soon as a nucleus is more than just a single proton. *Sigh*
This video is incorrect. The Helium ground state wavefunction can be easily solved with pen and paper, no computers, using a series of variational ansatzes, and this is historically how the then-new quantum mechanics was verified. It's not even all that difficult, because the phase space is 3 dimensional. The first excited state is doable also.
this comment is imprecise. The pen-and-paper solutions to the helium wave functions are only crude approximations. Also, the phase space is not 3 dimensional (and in any case in quantum mechanics it is not generally convenient to work in phase space). The dimensionality of phase space is 6*N_of_bodies so the helium atom it's 18-dimensional (full problem) or 12-dimensional (clamped nucleus approximation).
@@luckyluckydog123 The wavefunction space after rotational reduction is three dimensional, and the variational solutions are not 'crude approximations', they are within 1% of the exact solution in the region of significant wavefunction variation even with pen and paper. Wavefunctions aren't over phase space, (which is 12 dimensional not 18 dimensional BTW, center of mass doesn't count) but over configuration space, which is 6 dimensional. Three of those dimensions are determined by rotational invariance, so the wavefunction you need to do variations on is in the three remaining dimensions. The functional form is restricted by the one-particle solution to be exponentially tailing off at large x, and a Pade-style rational function in the exponent gets you the rest of the variational wavefunction. It was done before computers in the 1930s getting Helium energies to better than 1% accuracy.
You looks like Gray man movie villain 🤟🏻
Please add subtitle 😭
But does a solution exist and is it unique? 🤔
When schrodinger equation is hard to solve just use path integral 😂
Yeah it’s pretty good
Please never spell Schrödinger like that. If you can't find the ö character in your keyboard or compose it with umlaut (double overdot) and o, do what German speakers do: spell it Schroedinger. But never Schrodinger. Respect for the famous physicist's name.
Hehe.... Potential wells, Step potential and quantum tunneling and I'm good to go.
So no one is going to talk about his evolving looks
Cool moustaches
you will never be freddy mercury.
no video
The cat is alive and dead both🙃#schrodinger
nice mustache!!!🥳🥸
Very depressing. Do you need a quantum computer to solve?
I really like your mustache
Unfortunately having good taste in men doesn't shield me from being dumb
YOUR BEARD!!!!!!!!!!!
Just cancel out I * that trident looking thing and you get E = H hat, easy peasy where's my money