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Quantum Mechanics: Particle in a Box Periodic BC's

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data
    The question says to solve the Schrodinger equation for a particle in a box with periodic conditions and then it gives.
    ψ(0)=ψ(a)

    3. The attempt at a solution
    I used the above BC and I also did it as its derivative. (It wasn't stated but I assumed it was implied. I had no other way to solve for anything.)

    Here is my work..
    http://imageshack.us/a/img853/9774/qmproblem2.jpg [Broken]

    I was able to get the Energies, but I now have nothing left to solve for A and B! I was thinking of setting ψ(0)=0 or ψ(a)=0 but I don't know if this is correct because it is the same as the non-periodic condition.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 22, 2012 #2
    Hi.
    A box is bended so that point x=0 and point x=a coincide. derivatives and value of wave function coincide there. That might be an interpretation for your question.
     
  4. Sep 22, 2012 #3
    The norm of the wave function must be 1. This is the missing condition.
     
  5. Sep 22, 2012 #4
    I did the normalization and came to the following...
    [tex]A=\sqrt{\frac{2}{a}-B^2}[/tex]

    I still need one more condition to solve for A and B....
     
  6. Sep 22, 2012 #5
    You have two unknowns, A and B. You have two equations relating them with each other and a. I do not think you need anything else.
     
  7. Sep 23, 2012 #6

    vela

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    There are three unknowns: A, B, and k. You might find it easier to understand if you write the solution in the form ##\psi(x) = A \cos(kx+\phi)##. The normalization condition will allow you to solve for A, and like before, periodicity allows you to solve for k.
     
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