The Schrödinger equation

📚 The Schrödinger equation governs the time evolution of quantum states, just like Newton's second law of motion governs the time evolution of classical states. The key term in the Schrödinger equation is the Hamiltonian, the operator that describes the total energy of the system. In this video we discuss time evolution in quantum mechanics, and solve the Schrödinger equation for the special case of conservative systems in which the Hamiltonian is time independent.

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Director and writer: BM
Producer and designer: MC

[nomanahmadkhan]

Completed first playlist "postulate of quantum mechanics". From "nowhere in Q.M." to "feeling at home" is what this playlist has done. Thank you so much for your effort!

[TheWingEmpire]

Rigorous as it may be, quantum mechanics is really beautiful, and it's beauty is enhanced by the way you explain it.

[arisfluid]

Great videos, great channel! Keep up the good work!
Would be nice to add a video where you show how Schrondiger "constructed" this equation from scratch (like if we were inside Schrondiger's head), so the audience could understand the simplity that governs this equation but unravels so much about the state of a system!

[iotaphysics]

this is so interesting that i keep on watching without skipping

[ashrafabdelrahman]

Thanks for the videos. I would just suggest a big picture approach to study quantum mechanics and subsequently quantum field theory. As student, I have the motivation to understand the subject and approach it directly but I think students are overwhelmed by the information available so I think it would be very helpful if you can provide something like map. Thank you once again

[aesopw]

your videos are amazing
I have watched many youtube lecture playlists on QM in the past, some of which is perhaps at the postgraduate level
but I never felt so crystal clear about the concepts, before I discovered your channel

[davidroux]

I'm really enjoying and learning from your videos. I teach undergraduate QM, and wish I could explain this clearly! What a lot of hard work to make these videos, thank you for sharing.

[dcrespin]

I have seen half a dozen videos from this channel and all are excellent, this one is outstanding. Yours are the very best in YouTube about Quantum Mechanics. Three hurrah!s for rigorous Quantum Mechanics. My respects. However...

As you start explaining after 2:00, the linear Schrödinger Time Dependent Equation (STDE) is a postulate non deducible from other principles and is fully deterministic. The STDE:
1.- Has no stationary state (fixed point, singularity) other than the wave function identically zero.
2.- There are trajectories passing through any initial wave function; the eigenfunctions are not preferred in any obvious sense, beyond being periodic, which does not make them fixed points.
3.- The energy is constant along the trajectories in the space of wave functions hence no trajectories join states with different energies. This means that the wave function will never evolve starting at a given eigenfunction to end at an eigenfunction belonging to a different eigenvalue.

The above inconsistencies constituted an embarrassing situation for a time dependent equation aspiring to be a model of the hydrogen atom and motivated the creation (already in 1926) of the quantum postulates with the obvious intention of repairing the failures of the STDE, then to measurement theory, collapse of the wave packet, angular momentum where rotations are denied (spin), quantum electrodynamics, etc.

The most astonishing step taken by the founding fathers of QM was to keep the failed STDE as a valid physical Law of Nature. Perhaps they felt that such an equation, although dysfunctional and confusing, added an air of credibility to the newborn theory, and it did. But the STDE is so useless that you can eliminate it from the quantum postulates, keep the self adjoint energy operator H and thus obtain a "Purely Probabilistic Quantum Theory" (PPQT) where everything follows from the remaining quantum postulates.

All that said, it could well be the case since the STDE is simply postulated and does not predict the physical phenomena it is modelling, that the STDE is definitely wrong. If it actually is such a mistake then the quantum axioms, with the probabilistic interpretation included, could become a historically extraordinary system of fallacies.

It turns out that a Deterministic Time Dependent Equation (DTDE) does exist. It is non-linear, is based on Schrödinger self adjoint operator and has all the correct dynamical properties. With the DTDE everything is as causal, continuous and deterministic as any classical wave theory can be. Give it a trial.

The big question is how to overcome the instinctive resistance of the powerful and vigilant quantum establishment that needs to defend the theory (for them QM is a truth) and salvage their own scientific reputations.

For rigorous and technical details about these matters please google our paper entitled "Deconstruction of Quantum Wave Mechanics".

With cordial regards for both Professors M.
Daniel Crespin

[fernandojimenezmotte]

Thank You professor M does Science for your wonderful channel in Quantum Mechanics

[hassanchhaiba]

This is awsome. Thank you so much. I hope that you continue this great videos.

[redaabakhti]

among the countless ressources on Qm your lectures along with f.schuller's are among the the best of the best god bless you

[rubiramirez]

Wow, excellent channel!! One of the best explained, Have you ever considered talking about special relativity? It would be awesome ;D

[porit]

Now I understand conservation of the norm! Thanks a lot!😊

[Davide-blwb]

Hi your lectures are really great. Thank you very much, I have "fixed" a lot of things I got wrong in QM. Is there a preferential order to watch the videos? Do you make a printed version (slides/book) available?

[AlexAlex-fsbk]

Have you considered doing a video on the Dirac equation?

Great channel!

[nastyavicodin]

Thank you very much. Your way of explaining things is perfect!

[TheSADDAM]

I have a question. If the state of a system is unknown at first. Then we make a measurement and found \labmda_n, the system will immediately collapse into state un, which is an eigenstate. So, according to time evolution, the system will then stay in this eigenstate forever with global phase factor, right? So, any time we measure again, we should get the same value \lambda_n?

[ajilbabu]

What are the different representations of SE?
You mentioned the energy representations, are there any other?

[zhongfenglin]

Hi Professor M, thanks for your great video. I just have one question. At 14:48, I wonder if you forget to add a minus sign when |psi(t)> = exp[iEn(t-t0)/hbar] |un>, it should be |psi(t)> = exp[-iEn(t-t0)/hbar] |un> in my opinion. Am I correct? Or do I miss something?

[Bloodwork-igdg]

Your videos are great! Is there any literature on rigorous qm that you could recommend?