A beam of particles of energy E and incident upon a potential step of  is described by the...

A beam of particles of energy E and incident upon a potential step of  is described by the wave function

The amplitude of the wave (related to the number incident per unit distance) is arbitrarily chosen as 1. (a) Determine completely the reflected and transmitted waves by enforcing the required continuity conditions to obtain their (possibly com­plex) amplitudes, (b) Verify that the ratio of reflected probability density to the incident probability density agrees with equations (6-7).