Quantization of a phenomenological viscous force

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Abstract
We present a quantum version of the classical phenomenological concept of viscosity different from those given by Feshbach and Tikochinski and by Ghosh and Hasse. It is also based on the method of dual coordinates, and we show that the problems which arise from quantizing the bilinear Hamiltonian due to the unphysical nature of one of the degrees of freedom can be circumvented. The idea is to extract from the method the correct dynamics for the physical degree of freedom only. Demanding the correct quantum behavior for this degree of freedom in the frictionless limit specifies to a large extent the role played by the unphysical degree of freedom and leads to very reasonable results also for the classical limit of the free particle subject to a linear viscous force.

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