Hamiltonians and Expectation Values and Ehrenfest's theorum, OH MY ()

[Kvm90]

Homework Statement

(a) Let Q be an operator which is not a function of time, abd Let H be the Hamiltonian operator. Show that:

i(hbar)($$\delta<q>$$ / dt =<[Q,H]>

Here <q> is the expectation value of Q for any arbirtary time-dependent wave function Psi, which is not necessarily an eigenfunction of H, and <[Q,H]> is the expectation value of the commutator of Q and H for the same wave function.

Homework Equations

I know the Hamiltonian and I understand that [Q,H]=QH-HQ
so <QH-HQ> = int(Psi*(x,t)(QH-HQ)Psi(x,t) dx) and now I'm in over my head/don't really know whether what I'm doing is right.

The Attempt at a Solution

I'm having trouble getting anything further than what I mentioned above

 

[fzero]

Start with the left-hand side. Write down an expression for the expectation value $$\langle Q \rangle$$ and take the time derivative. You'll want to use Schrodinger's equation to connect to the expression on the right-hand side.