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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:
(1.1)
We divide space into three regions as shown in the figure below:

In region (1) and (3) the equation is:
(1.2)
Rewriting:
(1.3)
Where
(1.4)
The solution to this harmonic equation is:
(1.5)

And:
(1.6)
However, since in region (3) we do not expect a wave moving to the left, we can already state that
(1.7)
And therefore:
(1.8)
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

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