05. Development of Heisenberg's matrix mechanics

0:00 Recap of previous videos
4:50 Overview
11:44 Adiabatic hypothesis
14:55 Action-angle variables
21:47 Bohr's correspondence principle
26:18 Dispersion
35:52 Thomas-Reiche-Kuhn sum rule
38:43 Matrix mechanics
45:56 Heisenberg's equation of motion
47:29 The canonical commutation relation
53:13 Matrix derivatives and commutators
58:40 Commutator and Poisson bracket
1:05:40 Rederiving results with matrix mechanics
1:10:17 Normal Zeeman effect
1:14:23 Pauli's calculation of hydrogen energy levels
1:14:47 Runge-Lenz vector
1:17:38 Quantum Runge-Lenz vector
1:23:21 Relate quantum RL vector to energy
1:32:26 Summary

[eigenchris]

Thanks so much for putting in the time to make this video! I've tried looking at Heisenberg's original paper on matrix mechanics, but it's incomprehensible. It's great to have everything, including the motivations, laid out like this.

[worldhaseverything]

You explain me entire University physics course in free, thank you❤❤

[maximusideal]

This answers so many questions I had about the transition from old quantum mechanics to current QM for so long!

[MrFischvogel]

This is great! I tried to understand Heisenberg's magical paper for so long.
This really helps! =)) THANK YOU SO MUCH, SIR

[skbhatta]

I enjoyed the video and thank you very much. I am trying to relearn all the things that I tried to learn in my university days from your great explanations. Thanks

[JohnSmall]

This is superb!

I wish I could give more than one upvote.

It's exactly what I wanted to learn about to clarify a lot of steps in the derivation of quantum mechanics.

[McRingil]

Wow, incredible work, never seen put eberything in such an order.

[MarcoBarbato]

Fantastic lecture❤ I was trying to decode original Heisenberg paper, but now I understand that I miss some other element.

[baruchelgar]

Great video, thank you! I have a question about the content at minute 9:16. You mention that in the classical limit, the electron's radiation frequencies should coincide with its oscillation frequencies. The graphic shows a circular arrow emanating from the electron, suggesting that this oscillation frequency is related to its orbital motion around the nucleus. However, in the classical Lorentz model for dispersion, these frequencies are not related to orbital motion but are due to a restoring force acting on the electron when it's displaced from its equilibrium position. Is the graphic an oversimplification, or am I missing something?

[dag-vidarbauer]

Great lecture, but why did you remove your cover of anti-hero?😢

[jacobvandijk]

@ 1:33:42 How lucky we are nowadays! With QFT all our problems of visualization belong to the past. Be honest, who needs a picture when you read that an elementary particle is an unitary irreducible representation of the Poincare group? :-)