Scattering by a Square-Well Potential

particle energy E

1.5

potential well depth V

0

-1

potential well width a

5

-1.0

-0.5

0.0

0.5

1.0

E

0.5

1.0

R

T

-10

-5

5

10

-4

-2

2

4

E =

1.5

V

0

=

-1

a =

5

A beam of particles of unit amplitude moves across a well from the left. After scattering, a fraction

T

of the incident beam is transmitted through the well and the remaining fraction

R=1-T

is reflected. The interference of the reflected and incident beams shows a characteristic interference pattern to the left of the scattering region. To the right of the scattering region, only the transmitted wave appears, and there is no interference. Only in exceptional circumstances is the well transparent to the incident beam.The energy—real part (green), imaginary part (blue), and square of the wavefunction (orange)—is shown as functions of position in the lower graphic.