The quantum under-, critical- and over-damped driven harmonic oscillators (Q2766270)

The authors treat the cases of under-, critical- and over-damping for the quantum driven harmonic oscillator. Following a survey of the classical version, they construct the quantum invariant operator for each case and evaluate their eigenvalues. Using these eigenvalues and the Schrödinger equations, the wavefunctions are obtained for each case. From formal path integral theory, their propagators are evaluated and are checked with those obtained by the closed property formed by the complete set of wavefunctions.