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1
vote
1answer
178 views

What does Ehrenfest's theorem actually mean?

I am told that Ehrenfest's theorem, applied to a physical observable $\hat A$, is: $$\frac{d\langle\hat A\rangle}{dt}= \frac{i}{\bar h}\langle[\hat H,\hat A]\rangle$$ I don't understand how to use ...
0
votes
1answer
44 views

Relationship between the Galilei Group and the Phase Space

This question is kind of a follow up question to my last question on the need for canonical commutation relations and conjugate observables. A comment from Valter Moretti suggested that, given a ...
0
votes
0answers
43 views

What are some examples of classical observables that change with observation?

I was reading H. Moysés Nussenzveig "A course in basic physics, Volume IV" and in chapter 8, he is introducing the basic ideas of quantum mechanics, where he states that: In quantum mechanics, one ...
5
votes
1answer
176 views

In what sense (if any) is Action a physical observable?

Is there any sense in which we can consider Action a physical observable? What would experiments measuring it even look like? I am interested in answers both in classical and quantum mechanics. I ...
0
votes
1answer
511 views

Lie Algebra of Classical Observables under Poisson Bracket

I am confused with understanding the fundaments of classical mechanics. All classical observables commute since they are represented by regular functions on phase space. All classical observables form ...
2
votes
1answer
200 views

What exactly is the relationship between the algebraic formulation of Quantum Mechanics and the geometric formulation of Classical Mechanics?

Okay so if we consider a particular physical system, the classical description of the system starts by first introducing a symplectic manifold, which is the cotangent bundle of a configuration ...
10
votes
1answer
790 views

In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
10
votes
2answers
6k views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
3
votes
4answers
784 views

Complete set of observables in classical mechanics

I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case: The functions $q^k$ and $p_l$ form a complete ...
6
votes
3answers
574 views

Some questions on observables in QM

1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable? 2-What are the criteria to say whether ...