# Potential Barrier Question

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Consider the potential barrier

v(x) = + Vo, |x| < a

0, |x| > a

Solve for the transmission T and the absolute square |T|^2 for both cases E < Vo & E > Vo. Express the answer as |T|^2(x), where x = (2mEa^2)/h^2 = 1.

Plot |T|^2(x) for both E <Vo & E > V.

*Note: Please plot both cases on the same graph.

(see attachment for equations written in symbols)

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#### Solution Preview

Please see the attached file.

The way to solve this problem is writing the wave function in each region in the form Aexp(ikx)+A'exp(-ikx)

Then we have to satisfy 4 continuity conditions:

The functions and ...

#### Solution Summary

The transmission coefficient is worked out using the out-going and in-going amplitudes, with calculations provided step by step in an attached Word and PDF copy.

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