05. Development of Heisenberg's matrix mechanics

Slides and transcripts: drive.google.com/drive/folder...
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.

[@MrFischvogel]

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

[@worldhaseverything]

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

[@maximusideal1525]

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

[@skbhatta1]

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

[@lepidoptera9337]

Unless you were doing science history in university, the "derivation" won't help you much because it is physically not correct (but Heisenberg would not have been able to know that at the time). The structure of quantum mechanics does not come from this kind of reasoning, even though it dominated the early guesswork. In hindsight we can only say the founders guessed the correct solution but they arrived at it by all the wrong means. Today we know better, but we still teach it wrong. Having said that, certain aspects of Heisenberg's formalism are far closer to the actual facts than e.g. the Schroedinger/von Neumann approach.

[@gfygber9639]

a very well put together lecture

[@JohnSmall314]

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.

[@KarlFredrik]

Brilliant video! Thanks!

[@adityasrivastava9416]

amazing lecture!!!!

[@McRingil]

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

[@user-kc2iu8df4p]

Think you so much great work

[@MarcoBarbato]

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

[@SanderKonijnenberg]

Thanks for the comment, I've made the slides and transcript available here: drive.google.com/drive/folders/1TFzYibPY8t9y4jH84Ifq-l-3NJjB_cHt?usp=drive_link

[@3339LuXz]

I love you

[@dag-vidarbauer80]

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

[@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?

[@SanderKonijnenberg]

That's a good question. You are correct that Lorentz' model does not make reference to circular orbits. Lorentz developed his model around 1900 (at least before his Nobel Prize in 1902), while Rutherford formulated his model of the atom (with electrons orbiting a small nucleus) in 1911. So Lorentz was probably thinking in terms of electrons vibrating in something like Thomson's plum pudding model. Nonetheless, the key point is that in Lorentz' model the radiation frequency is still related to the mechanical motion of the electron, as required by classical electrodynamics. The fact that this motion later turned out to be an orbit rather than a vibration is, I would say, of lesser relevance.

[@baruchelgar]

Clear. Thank you!@@SanderKonijnenberg

[@lepidoptera9337]

First of all the idea of periodic motion in an atom is 100% wrong. The observed energies/oscillation frequencies are NOT the ones predicted by quantum mechanics for the electronic states but they are the differences in energies/frequencies between some of those states. The deeper reason for this won't be clear until we develop a quantum field theoretical picture of microscopic processes. Most non-relativistic textbooks are neglecting to discuss this disconnect completely, if I remember correctly. It is only discussed reasonably well in atomic physics textbooks.

[@jacobvandijk6525]

@ 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? :-)

[@lepidoptera9337]

There are no particles in quantum mechanics. There are only quanta of energy. The fields are representations of the Poincare group (-ish... there is a bit of a complication there). There is, technically, nothing to visualize. Quantum mechanics is an ensemble theory, i.e. physical measurements belong to completely independent copies of the same experiment. One can derive much of the structure of the theory from that alone (via Kolmogorov's axioms). The remainder is, as you said, relativity. It follows that a direct derivation of non-relativistic QM is not possible. It won't lead to a self-consistent theory.

[@jacobvandijk6525]

@@lepidoptera9337 Agreed. That's what I meant with "who needs a picture of a particle". A particle is just a collection of properties. No visualisation needed. We describe visible nature with invisible concepts ;-)

[@lepidoptera9337]

@@jacobvandijk6525 There is nothing invisible about energy. It performs work.

[@nathaliearthur6162]

*Promo sm*