Abstract
We consider a class of time-dependent harmonic oscillators, H(t)=p2/2mtalpha + m omega 2tbq2/2, 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.