Electron In An Infinite Potential Well

[sattomon]

Homework Statement

An electron is in a Infinite potential well (1-dimensional box with infinite wall boundary conditions) at the second energy level. The width of the box is L. What is the electron density n(x) as a function of the position x?

Homework Equations

time-independent Schrödinger equation:

general solution:

The Attempt at a Solution

From http://en.wikipedia.org/wiki/Particle_in_a_box#1-dimensional_box"

I'm not sure what the next step is. I'm confused with the wording "electron density n(x)". Does this mean probability (i.e. $\|\psi_n(x)\|^2$)?

 

[Dick]

Yes, it does.

 

[sattomon]

So does that mean$n(x)=\|\psi_n(x)\|^2$ ?

 

[Dick]

Yes,
$n(x)=\|\psi_n(x)\|^2$