On the Quantization of Damped Harmonic Oscillator

We derive results for two constants of the motion of a one-dimensional damped harmonic oscillator with position-dependent frictional coefficient and use them to obtain two alternative Lagrangian representations, which are not connected by a gauge term. The Hamiltonians corresponding to these Lagrangians lead to canonically inequivalent phase-space descriptions. We could, however, make use of a perturbation theoretic approach to quantize the classical motion using both Hamiltonians and thus demonstrate that the corresponding quantum systems are entirely different. (author)