ON THE BEHAVIOR OF QUANTUM-SYSTEMS WITH TIME-DEPENDENT BOUNDARY-CONDITIONS

We discuss some properties of a quantum oscillator with time-dependent frequency, bouncing between a fixed and an oscillating wall. This model is an exactly solvable modification of the classical Fermi accelerator. Its further modification, including a time-dependent force exerted on the oscillator, is also suggested and the corresponding non-stationary Schrodinger equation is exactly solved. Extensive computer calculations of the time evolution of wave packets and average kinetic energy lead, for the former simpler model, to a number of rather surprising results.