Expectation Values for momentum and a particle in a square well

[muffins08]

Homework Statement

Calculate the expectation values of p and p² for a particle in state n=2 in a square well potential.

Homework Equations

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

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

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?

 

[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.

 

[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!