Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational field with linearly or quadratically damped motion. In each case, we study the evolution of Gaussian wave packets and discuss the characteristic features that help us distinguish between different types of damping. For quadratic damping we show the connection of the action and equation of motion to a zero-dimensional version of a scalar field theory. We also demonstrate that the equation of motion for quadratic damping can be identified as a geodesic equation in a fictitious two-dimensional space.
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2007
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