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2
votes
2answers
70 views

Are $\hat x$ and $\hat p$ assumed to be time-independent operators?

In the book Quantum Mechanics by Cohen-Tannoudji, at $G_{III}$, it is given that and then in the comment section, it is also given that so I'm pretty confused in here, because in one side, they say ...
1
vote
1answer
227 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 ...
4
votes
1answer
169 views

How come there are Schrödinger Picture operators with explicit time dependence?

In the Schrödinger picture, observables are said to be time independent (see Cohen, for example) operators. However, when deriving the Heisenberg Equation of Motion $$i\hbar\frac{d}{dt}A_H(t)=[A_H(t),...
2
votes
4answers
183 views

Why does the time-evolution operator $U(t)$ depend explicitly on time in the Schrodinger picture?

Schrodinger's picture is that operators are time-independent. But time evolution operator $U(t)$ is time-dependent. Why is that?
2
votes
1answer
325 views

Is it obvious that the Hamiltonian observable in Quantum Mechanics should also be the Energy observable?

In Quantum Mechanics, the Hamiltonian observable is defined as the generator of time translations. It's easy to show that if we take this to be the definition of the Hamiltonian, then it is of the ...
-2
votes
2answers
50 views

What is the correct *first* interpretation of the time derivative of some measurable quantity?

For example, take the position function $x(t)$. When I take $(d/dt)(x(t))$, I know that I must ultimately conclude that the result is the velocity function $v(t)$. But this feels like a ''jump ahead'' ...