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Particle moving in a delta potential

A particle of mass m, with energy E>0, is moving in the potential
V(x)=g[delta(x+a) + delta(x-a)]

Assuming that the particle is incident from the left, what is the solution of the Schrodinger equation in all three regions (x<a, -a<x<a, x>a) for this situation? Also, what are the appropriate continuity conditions at x=+a and x= -a?

Solution Preview

See attached files.
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usepackage{graphicx,amsmath,amssymb}
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begin{document}
title{Particle moving in a delta potential}
date{}
maketitle
The Schr"odinger equation is:
begin{equation}label{sch}
-frac{hbar^{2}}{2m}frac{partial^{2}}{partial ...

Solution Summary

We explain how to solve the Schrödinger equation for the potential V(x)=g[delta(x+a) + delta(x-a)]. We consider the case of an unbound particle with positive energy.

$2.19