Unraveling the Mystery of Quantum Mechanics: Square Wells & Momentum

[Ze Corndog]

Homework Statement

Here's an image
http://i.imgur.com/oC8Y6.jpg

Homework Equations

The wave function for an infinite square well, the expectation values and operators for momentum and I guess the normalization condition? I don't really know because I don't understand the question.

The Attempt at a Solution

I don't understand what I'm being asked there exactly. It just doesn't seem clear to me at all. What does that notation for the momentum mean? I figured Px is the one-dimensional momentum in the x-direction, but what's that N superscript? I've never seen that notation anywhere in my textbook or even in the lectures... does it mean Px for any N?

What's in an eigenstate of the energy? I'm assuming the particle... but what's that mean? The energy is En for any n?

I'd like to be able to do this on my own but this is probably the most unclear question I've ever had in physics. It also doesn't help that this is the first QM problem I'm encountering.

Isn't the expectation value of Px just 0? That's what my textbook says, but that doesn't seem like what I'm being asked to find... or is it?

 

[Jorriss]

It's a one dimensional box so the Px seems redundant. Anyhow, it seems it is asking you to find the expectation value of momentum raised to some power. So, yes, find Px for N being 1,2,3,4 etc ie find < p >, < p^2>, etc.

You seem to have the right idea.

You are right that < p > = 0, but < p^2 > is not zero.

 

[Ze Corndog]

So do I just have to solve for a general expression of <p^N>?

 

[Jorriss]

That's how I interpret it.

 

[Ze Corndog]

Thanks for clearing that up

What about this one?
http://i.imgur.com/0hq6l.jpg
I'm guessing that means 0.5*<a function of position*momentum + momentum*position>
isn't the function just <2*x*p>?
and then taking half of that would just be <x*p>

that's the way I see it, but I feel like I'm wrong