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Double delta-function potential

  1. Oct 22, 2011 #1
    My session expired while typing this post, so this is my second attempt at typing it. I *always* forget to paste into notepad before submitting these darned things.
    1. The problem statement, all variables and given/known data

    Problem 2.27, Griffiths.

    Given two delta potential wells at +a and -a, determine the number of bound states, find their associated energies, sketch the wave functions.

    2. Relevant equations

    [itex]V(x) = -\alpha\left[\delta\left(x+a\right)+\delta\left(x-a\right)\right][/itex]


    3. The attempt at a solution

    This is the first problem in the book where I really do not know where to begin. I know that the answer has to be in some form of exp(kt) where k is sqrt(-2*m*E)\hbar.

    I vaguely understand the book's process for the logic behind constructing the wave function for a single delta potential well, but clearly not well enough.
     
  2. jcsd
  3. Oct 22, 2011 #2

    vela

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    Start by solving the Schrodinger equation in the three regions x<-a, -a≤x≤a, and x>a.
     
  4. Oct 22, 2011 #3
    Thanks for the assistance. All I had to do was solve for a 0 potential and pay attention to the boundary conditions (continuous function, discontinuous derivative by a specific value).

    The hard part, after that, was not getting lost in the algebra. I still don't quite understand how to solve for the energy, though. I ended up with two equations that needed numerical solving, one for the even wave function, and one for the odd wave function.

    Overall, this problem was a real curve ball, and the specific questions this problem asked were far more confusing to me than any of the others.
     
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