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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 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.

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 ...

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