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Greens Function Solution of Schrodinger Equation

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Using the Greens function technique, reduce the Schrodinger Equation for the following potential:

    V = V0 , 0<x<a
    V = infinite, elsewhere.

    2. Relevant equations



    3. The attempt at a solution

    I have no idea what "reduce" means. The professor did not go over this and internet searches revealed nothing about this.

    Does this mean put the Schrodinger equation in the form Hψ(x) = Eψ(x), then setting a Greens function G(x) such that HG(x) = δ(x-s) with the boundary conditions 0<s<a and G(0)=G(a)=0, and using the integral formula u(x) = ∫ G(x,s)f(s)ds for Lu(x) = f(x) where L is a linear differential operator?

    In our case L = H, f(x) = Eψ(x)

    So the final equation would be ψ(x) = ∫ G(x,s)Eψ(s)ds

    But the question does not ask to solve for ψ(x), it said REDUCE... is REDUCE the same as solve?
     
  2. jcsd
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