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.