Condition for expectation value of an operator to depend on time

[AlexCdeP]

Homework Statement

A particle is in a 1D harmonic oscillator potential. Under what conditions will the
expectation value of an operator Q (no explicit time dependence) depend on time if
(i) the particle is initially in a momentum eigenstate?
(ii) the particle is initially in an energy eigenstate?

Homework Equations

The first two parts of this question required me to show that

$\frac{d}{dt}$<Q> = $\frac{i}{hbar}$ <[H,Q]> + <$\frac{d}{dt}$Q>

Q is any hermitian operator. I did this fine and then derived the virial theorem from this, which is where the rate of change of the expectation for Q is zero. I'm assuming I'm supposed to use this equation to find the conditions, but to be perfectly honest I have no idea how to approach this at all.

I know that if the operator commutes with the Hamiltonian H then it will have no dependence on time, but how can I use this to answer the question?

 

[davidchen9568]

Please delete this post.

 

[AlexCdeP]

Please delete this post.

Thanks for the help david, what a complete waste of both of our time. Maybe it's far too obvious for you? I have no idea what's wrong with my post, so it'd be great if you could enlighten me.

 

[vela]

I think David meant he wanted his post deleted, not your thread.

 

[AlexCdeP]

Oh sorry, apologies if that's the case.