# Quantum Mechanics Problem

1. Mar 11, 2007

### G01

1. The problem statement, all variables and given/known data
Consider the potential:

$$V(x) = \alpha\delta(x)$$ -a<x<a
$$V(x) = \infinity$$ |x|>a

Analyze the even and odd solutions separately, and find the allowed energies.

2. Relevant equations

3. The attempt at a solution

So far, I looked at the even solutions:

$$\psi(x)=A\cos(kx)$$ 0<x<a
$$\psi(-x)$$ -a<x<0

With this solution, Acoskx must equal zero at the delta barrier correct?
Since the only way this could happen is for A=0, am I to assume the even solutions don't exist?

2. Mar 11, 2007

### G01

I think I may be confused on what they mean by "the even and odd solutions."

Last edited: Mar 11, 2007
3. Mar 11, 2007

### Dr Transport

Solutions which are odd and even under coordinate inversion......

4. Mar 11, 2007

### G01

Ok I think I get that much, did I at least start this problem the correct way? Like, do I have the correct form of the even solutions?