Reflection off a reflecting surface in quantum mechanics. -III

Summary

This is the last of a series of papers dealing with the problem of reflection of a particle off a reflecting surface inquantum mechanics. The first two papers dealt with answering the question:where do the reflections actually occur on the reflecting surface? and in investigating the law of reflection as carried out in configuration space. The present paper deals with the study of the fate of the momentum of a particle and with establishing in the classical limit the law of reflection in terms of momenta when the skin depth of the reflecting surface is macroscopically small but is much larger than a quantum-mechanical scale introduced byħ. The latter follows by a systematic application of the time-dependent Green’s function in half-space.