# Homework Help: Particles Mean Momentum

1. Jun 9, 2007

### n0_3sc

1. The problem statement, all variables and given/known data

Particle in a 1D well of infinite depth, width 2a has wavefunction:
$$\psi = Asin(k_{n}x)$$
Its prepared in state:
$$\psi(x,t) = \frac{1}{\sqrt{2}} [\psi_{0}(x)+i\psi_{1}(x)]$$
I need to find the mean momentum as a function of time ie. prove this:
$$<\hat{p_{x}}(t)> = \frac{4\hbar}{3a} sin[\frac{3\hbar\pi^{2}}{8ma^{2}}t]$$

2. Relevant equations

I've worked out $$k_{n}$$ and the relevant normalisation constants...But I don't think its important to state them for my question since I need to know how to attempt this problem.

3. The attempt at a solution

I thought about doing it like this:
$$<\hat{p_{x}}>=\int\psi^*(x,t)\hat{p_{x}}\psi(x,t)\dx$$
where
$$\hat{p_{x}}=-i\hbar\frac{d}{dx}$$
...but this became far too tedious and I don't know where the 't' is meant to come in...
I also tried doing:
$$<\hat{p_{x}}>=m<\frac{d\hat{x}}{dt}>$$
(Ehrenfest's Theorem) but no luck...

Any guidance will help...