All Questions

10 questions
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...