Electron In An Infinite Potential Well

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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:
f4df6d1f1c5ead81edcf7dcf6b35457b.png

general solution:
5f2c4c4916b96ecd830ddda628f103f5.png


The Attempt at a Solution



From http://en.wikipedia.org/wiki/Particle_in_a_box#1-dimensional_box"
06571133afb27204cd0785da860df16b.png

5464deee159d922f51c081d408951169.png


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)?
 

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Yes, it does.
 
So does that meann(x)=\|\psi_n(x)\|^2 ?
 
Yes,
<br /> n(x)=\|\psi_n(x)\|^2<br />
 

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