- #1

andre220

- 75

- 1

## Homework Statement

Prove that for any stationary state the average of the commutator of any operator with the Hamiltonian is zero: [tex]\langle\left[\hat{A},\hat{H}\right]\rangle = 0.[/tex]

Substitute for [itex]\hat{A}[/itex] the (virial) operator:[tex]\hat{A} = \frac{1}{2}\sum\limits_i\left(\hat{p}_ix_i +x_i\hat{p}_i\right)[/tex]

and prove the virial theorem.

## Homework Equations

##[\hat{A},\hat{H}] =\hat{A}\hat{H}-\hat{H}\hat{A}##

## The Attempt at a Solution

So for stationary states we have that ##H(q_i,\dot{q}_i,...)##, namely ##H## is not a function of ##t##, and we know that the commutator ##[\hat{A},\hat{H}] =\hat{A}\hat{H}-\hat{H}\hat{A}##. For any operator ##\hat{A}## the expectation value ##\langle\hat{A}\rangle = \langle\psi\mid\hat{A}\psi\mid\rangle##, where ##\psi## is some given state. So I'm stuck as to where to start. Initially my thought is to take ##\frac{\partial \hat{A}}{\partial t}##, but I don't know where that will get me.