ON THE PROPAGATORS FOR HARD-WALL POTENTIALS OSCILLATING PERIODICALLY WITH CONSTANT VELOCITY

Exact propagators for some moving hard-wall potentials with constant v elocity have been previously found by the authors. Here, applying the semi-group property to these propagators, we first evaluate the exact propagators for the two one-dimensional quantum oscillating systems; ( A) a free particle interacting with one hard-wall potential oscillatin g periodically with constant velocity, and (B) the Fermi-acceleration model with one wall oscillating periodically with constant velocity. W e then discuss the energy of the system (B) by calculating its transit ion amplitudes. Finally, we analyse the classical paths and show that the semiclassical approximation to the propagators is not valid any mo re for the quantum oscillating systems considered.