# Momentum Space Wave Function

1. Jan 30, 2005

### RPI_Quantum

How exactly does one find a wave function? Specifically, I am asked to find the momentum space wave functoin for the nth stationary state in an infinte square well. Then I am to graph the probability density (phi sqaured) for the first and second energy levels. Lastly, I need to use the momentum space wave function to find the expectation value of p^2.

For finding the expectation value, I assume that I need to integrate using p^2 as an operator between phi and phi*, just as I would if I was using the regular position wavefunction. Is this right?

Anyway, what I really need help with is finding a wave function, and graphing the probability densities.

2. Jan 30, 2005

### dextercioby

For the last question,yes u can use each of them...But with caustion.Remember the Parseval equality...

Solve the HE in the coordinate representation and then transfourier the wave function...

Daniel.

3. Jan 30, 2005

### RPI_Quantum

Hope I don't sound dumb, but I really have no idea about what you are saying. A lot of the math terminology was never taught to me, so even as I am trying to pick it up, some things escape me.

This seems like a fundmental question, which I have no idea about: where does the wave function come from? In the particular question that I am working on I am coming up with a wave equation for a square well.

4. Jan 30, 2005

### mikeu

Wavefunctions are found as solutions to the Schrödinger wave equation, subject to the particular boundary conditions of the system you are looking at. These conditions usually include things such as the wavefunction must be continuous as it crosses the boundary between regions of different potential.

As for finding the wavefunction in momentum space instead of position space, what dextercioby meant was that you can perform a Fourier transform between the two spaces, so if you know one the other isn't too hard to find.

There should be plenty of examples on the web if you just google 'square well potential' or something similar, and perhaps check mathworld for info on Fourier transforms. If your well is infinite, be sure to include that since it's a slightly simpler solution.