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    Transmission coefficient of the finite square well

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    A particle of positive energy approaches the square well illustrated in fig 3.5 - attached- from the left. some of the wave will be transmitted and some will be reflected.

    a) calculate the transmission amplitude
    b) show that the transmission amplitude equals 1 when 2k'L = npi, where k'= [sq rt ((2m(E+V_0))/h-bar] is the wavenumber in the region of the well. thus the potential well becomes transparent at a discrete set of energies (Ramsauer effect).

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    Solution Preview

    Schrodinger equation is valid everywhere.
    It is:
    We divide space into three regions as shown in the figure below:

    In region (1) and (3) the equation is:
    The solution to this harmonic equation is:

    However, since in region (3) we do not expect a wave moving to the left, we can already state that
    And therefore:
    Over the well, the ...

    Solution Summary

    The 6-pages solution shows how to obtain the transmission coefficient for the finite symmetric square well when E>0