TIME EVOLUTION OF HARMONIC-OSCILLATORS WITH TIME-DEPENDENT PARAMETERS- A STEP-FUNCTION APPROXIMATION

The time evolution of a quantum harmonic oscillator with a series of s udden jumps of the mass or the frequency is determined in the form of a recursion relation. An approximating method is developed for determi ning the time evolution of harmonic oscillators with arbitrary derivab le functions of the frequency or the mass. The approximate solution is shown to tend to the analytical one in the limiting case. As a demons tration of the approximating method, the solution of the problem of da mped oscillation in the square of the oscillator frequency is presente d.