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Electron In An Infinite Potential Well

  • Thread starter sattomon
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  • #1
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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. [itex]\|\psi_n(x)\|^2[/itex])?
 

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Answers and Replies

  • #2
Dick
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Yes, it does.
 
  • #3
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So does that mean[itex]n(x)=\|\psi_n(x)\|^2[/itex] ?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Yes,
[itex]
n(x)=\|\psi_n(x)\|^2
[/itex]
 

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