Quantum mechanics particle in a well

[kcasali]

Homework Statement

Given is an infinite square well potential. V=infinity at x=a, x=-a. V=0 between -a and a. Take an even state u=Ccos(kx), and find <x>,<x^2>,<p_x>, and <(p_x)^2>. Your final answers should not contain k, which will be eliminated by the boundary conditions.

Homework Equations

The Attempt at a Solution

I'm really just generally confused by this question, and I need a nudge in the right direction.

I know how to find the wavefunction and energy if the well is between 0 and a, how do I find it between -a and a? Can I just redefine the coordinate system so that the well is between 0 and 2a? Also, what does he mean by an even state? That the energy is in an even state?

 

[Amok]

What boundary conditions did you use when you solved the problem in the case where the well is 0 and a? My guess is that you required that the wavefunction go to zero at 0 an a. Do the same for -a and a and you should be ok. An even state means that the quantum number is even.

 

[vela]

An even state means that the quantum number is even.

That's not correct for this problem.

An even state is where the wave function is even, i.e. f(x)=f(-x).

 

[Amok]

True, sorry about that.

 

[kcasali]

I figured it out, thanks for the help. :)