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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)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:58 pm ad1c9bdddf


    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.