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Quantum Mechanics: Particle in a Box Periodic BC's

  • Thread starter Xyius
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  • #1
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Homework Statement


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)

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.
 
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Answers and Replies

  • #2
1,225
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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.
 
  • #3
6,054
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The norm of the wave function must be 1. This is the missing condition.
 
  • #4
508
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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....
 
  • #5
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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.
 
  • #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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