# Expectation values in momentum/position space?

1. May 10, 2004

### clumsy9irl

I'm currently, yet again, left clueless by a problem.

See: the actual equations here

Ok, so they give the Psi(x) in position space, and the first question is to give the corresponding, normalized wave equation in momentum space.

You do a fourier transform, no?

Psi(p)=Int ((1/sqrt2pi) Psi(x) (e^ipx/hbar) dx

no?

From that, I get Psi(p)=(2hbar/(p sqrt2pi)) sin (pa/hbar)

or....?

After that, I tried to get the expectation value, <p>, but with poor results. Integrate Psi* Psi p dp, yeah? What I get is 4hbar^2/(2pi p^2) [ln|p| sin^2(pa/hbar)]

Now, I know this has to be wrong, but I have no idea what I'm doing to screw it up.

I tried to do <p^2> and <x> and it just gets worse, and messier. WHAT AM I DOING WRONG??

Pleease help. Thank you :)

edit: I think I've got it! Well, at least part of it. I've gotten my expectation values for p and x to be zero, and I think my x^2 and p^2 are wrong, but... I can't think of anything else... so, it's staying right now with

<p^2>= (2hbarp*sinpa)/pi

<x^2>= A^2 (2a^3/3)

Working on the rest, still... but coming a bit further?

Last edited: May 10, 2004