# Finite Square Well/ Barrier

## Homework Statement

Determine the transmission coefficient for a rectangular barrier. Treat seperately the three cases E<Vo, E>Vo, and E=Vo.

## Homework Equations

V(x)= +Vo if -a<xa
V(x)= 0 otherwise

Transmission coefficient=(amplitude of transmited wave)2/(amplitude of incoming wave)2

I am also using the Time independent Schrodinger equation

## The Attempt at a Solution

What I did for each case was to solve the Schrodinger equation in the following regions:

a) x<-a
b) -a<x<a
c) x>a

After doing this I exploited the fact that my solutions had to be continuous at the boundaries. The derivatives also had to be continuous at the boundaries.

ie)$$\Psi$$(a)-=$$\Psi$$(a)+ and,

d/dx($$\Psi$$(a)-)=d/dx($$\Psi$$(a)+

After doing this I get a bunch of equations and my goal is to isolate the amplitude of transmiited wave function and the amplitude of the initial wave function. I think that after a bunch of tedious algebra I will be able to isolate for the desired things.

Is there an easier way to isolate my amplitudes? My professor mentioned something about treating the even and odd solutions of the wavefunctions seperately, but I do not know what he means.

If any of this is unclear please let me know!

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