# Quantum Mechanics Problem

Homework Helper
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## Homework Statement

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.

## 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?

Am I going about this correctly? Thanks for any help you can offer.

## Answers and Replies

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

Last edited:
Dr Transport
Science Advisor
Gold Member
Solutions which are odd and even under coordinate inversion......

Homework Helper
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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?