A CLASS OF EXACTLY SOLVED TIME-DEPENDENT QUANTUM HARMONIC-OSCILLATORS

We consider a class of time-dependent harmonic oscillators, H(t) = p2/2mt(alpha) + momega2t(b)q2/2, whose mass and frequency vary as non-negative powers of time. Classically they describe damping oscillators slowly decaying as negative powers of time. Using the connection between classical and quantum harmonic oscillators we find analytically the Lewis-Riesenfeld invariants, obtain the exact quantum states, and compare these with the Caldirola-Kanai oscillator.