# Expectation Values for momentum and a particle in a square well

1. Aug 31, 2011

### muffins08

1. The problem statement, all variables and given/known data
Calculate the expectation values of p and p2 for a particle in state n=2 in a square well potential.

2. Relevant equations

$\Psi$(x,y) = (2/L)*sin(n1$\pi$x/L)*sin(n2$\pi$y/L)

p= -i$\hbar$$\partial$/$\partial$x

3. The attempt at a solution

$\int$$\Psi$p$\Psi$dxdy limits being from 0 to L for both.

I derived the two dimension wave equation using separation of variables. This is where I had some questions. For the state n=2, does that mean both n1 and n2 equal 2 or does one of them equal 1 and the other 2 since from what I understand 1,2 would be the next highest energy level. Also as I was integrating, the x portion integrated nicely due to the momentum operator while the y portion stayed rather "unclean". Was I suppose to apply the momentum operator in both the x and y direction?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 31, 2011

### Dick

I don't know what n=2 is supposed to mean for a two dimensional square well where you have two quantum numbers. Are you sure they don't mean a one dimensional problem? That's also called a 'square well' referring to the shape of the potential. Square doesn't necessarily mean two dimensions.

3. Aug 31, 2011

### muffins08

Completely forgot I posted here, and yes I just realized that it's just a one dimensional well after lots of thinking...it's been a long a day heh. Thanks for the input though!