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).
Schrodinger equation is valid everywhere.
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
Over the well, the ...
The 6-pages solution shows how to obtain the transmission coefficient for the finite symmetric square well when E>0