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Homework Help: Electron In An Infinite Potential Well

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations
    time-independent Schrödinger equation:
    f4df6d1f1c5ead81edcf7dcf6b35457b.png
    general solution:
    5f2c4c4916b96ecd830ddda628f103f5.png

    3. 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])?
     

    Attached Files:

    Last edited by a moderator: Apr 23, 2017
  2. jcsd
  3. Nov 22, 2008 #2

    Dick

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    Yes, it does.
     
  4. Nov 23, 2008 #3
    So does that mean[itex]n(x)=\|\psi_n(x)\|^2[/itex] ?
     
  5. Nov 23, 2008 #4

    Dick

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    Science Advisor
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    Yes,
    [itex]
    n(x)=\|\psi_n(x)\|^2
    [/itex]
     
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