# Qm problem II

1. Feb 3, 2005

### broegger

I am trying to prove that

$$\frac{d\langle p \rangle}{dt} = \langle -\frac{\partial V}{\partial x} \rangle$$

I am done if I can just prove that

$$\left[ \Psi^*\frac{\partial^2 \Psi}{\partial x^2} \right]_{-\infty}^{\infty} = 0$$

$$\left[ \frac{\partial \Psi}{\partial x} \frac{\partial \Psi^*}{\partial x} \right]_{-\infty}^{\infty} = 0$$

My suggestion is that since $$\Psi$$ is a wavefunction, it is normalizable and must approach 0 as $$x \rightarrow \pm\infty$$, and so must its derivatives. I don't know if this argument holds?

Last edited: Feb 3, 2005
2. Feb 3, 2005

### vanesch

Staff Emeritus

I would think that's a valid reason, no ?

cheers,
Patrick.

3. Feb 3, 2005

### da_willem

Good luck proving something incorrect! :tongue2:

4. Feb 3, 2005

### broegger

I see your point :) I mean the time derivative, of course.

5. Feb 3, 2005

### dextercioby

That's something totally different.It is simply CORRECT...

Daniel.

6. Feb 3, 2005

### vanesch

Staff Emeritus
No, it also excaped me, but of course what is correct is:

d/dt <p> = <- dV/dx >

cheers,
Patrick.