# Quantum Mechanics: Particle in a Box Periodic BC's

1. Sep 22, 2012

### Xyius

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. Sep 22, 2012

### sweet springs

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. Sep 22, 2012

### voko

The norm of the wave function must be 1. This is the missing condition.

4. Sep 22, 2012

### Xyius

I did the normalization and came to the following...
$$A=\sqrt{\frac{2}{a}-B^2}$$

I still need one more condition to solve for A and B....

5. Sep 22, 2012

### voko

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. Sep 23, 2012

### vela

Staff Emeritus
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.