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Infinite potential well with V(x)=Asin(x pi/a)

  1. Feb 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi, this is basically a particle in a box problem but V(x) is sinusoidal inside the box.

    V(x)=-Asin(pi x/a) 0<x<a
    V(x)=Infinity otherwise

    A: depth of the well

    In the question, it asks me to plot the first 4 eigenfunctions.


    3. The attempt at a solution

    After plugging the sinusoidal potential function into the Schrodinger equation, the equation looks like:

    y''(x)-(E+Asin(Cx)y(x)=0

    I don't have a clue about solving this. I've been looking at the quantum mechanics books and diff. eqs. books for hours but I can't seem to find anything useful. I'm using Mathematica I cannot solve it numerically since I don't know "E".

    Is there any place that I can look at for a possible solution or direction? Thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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