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

Xyius

## 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

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.

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

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....

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.

Staff Emeritus