MATTER WAVES AT A VIBRATING SURFACE - TRANSITION FROM QUANTUM-MECHANICAL TO CLASSICAL BEHAVIOR

We investigate the time-dependent Schrodinger equation for the case of a plane matter wave incident on an oscillating potential step. Approx imate solutions are given for different regimes of the problem. The re sulting energy spectra are quantized. This may either be interpreted a s a phase modulation of the wave or as a coherent multiphonon exchange . A comparison to the results that apply for a beam of classical parti cles is made. In particular, the transition from the quantum-mechanica l to the classical case is examined. We have performed an experiment w ith very cold neutrons that clearly revealed the discussed effects. En ergy splittings of 2.8 to 9.1 neV of the reflected waves were analyzed with an energy resolution of similar to 1 neV, thus demonstrating the feasibility of such high-resolution experiments with neutron reflecto metry.