3 ms·
Skimmed some of the articles, particularly those nearer to my field. Seems like a generally good set of informal notes. Random comments: >when the states evol
by dawnofdusk 3y ago
Skimmed some of the articles, particularly those nearer to my field. Seems like a generally good set of informal notes.
Random comments:
>when the states evolve in time and the observables don’t we are using Liouville’s picture; when the observables evolve in time and the states don’t we are using Hamilton’s picture.
I have never heard this terminology, I have only heard Schrodinger's picture vs. Heisenberg's picture.
>This means that, very unlike on a Riemannian manifold, a symplectic manifold has no local geometry, so there’s no symplectic analogue of anything like curvature.
Perhaps the only enlightening comment I have ever heard about the tautological 1-form/symplectic approach to Hamiltonian mechanics.
- nicf 3y ago> I have never heard this terminology, I have only heard Schrodinger's picture vs. Heisenberg's picture. I wrote the QM article a very long time ago at this point, and I actually can't reconstruct at the moment why I used those two names! I've also heard Schrodinger and Heisenberg much more frequently. Might be worth an edit.
- Someone 3y agoMaybe because Liouville and Hamilton, being mathematicians, are better known to the target audience than the physicists Schrödinger and Heisenberg? I know the difference between mathematicians and theoretical physicists can be small, but I think that categorization is valid. To verify my intuition, I checked Wikipedia. It calls - Liouville a mathematician and engineer (https://en.wikipedia.org/wiki/Joseph_Liouville https://en.wikipedia.org/wiki/Joseph_Liouville) - Hamílton a mathematician, astronomer and physicist (https://en.wikipedia.org/wiki/William_Rowan_Hamilton https://en.wikipedia.org/wiki/William_Rowan_Hamilton) - Schrödinger a physicist (https://en.wikipedia.org/wiki/Erwin_Schrödinger https://en.wikipedia.org/wiki/Erwin_Schrödinger) - Heisenberg a theoretical physicist (https://en.wikipedia.org/wiki/Werner_Heisenberg https://en.wikipedia.org/wiki/Werner_Heisenberg)
- remigius 3y ago[dead]