# Transmission coefficient of the finite square well

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).

https://brainmass.com/physics/schrodinger/transmission-coefficient-finite-square-well-564326

#### 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)

â€ƒ

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