Geodesic
Quantum-mechanical description of friction
Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 1, pp. 97-108

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Method of quantum description of dissipative systems based on the classical approach using friction forces is proposed. A Hamiltonian is obtained for motion with friction. The method is applied to the description of a linear oscillator with friction. The operator equations of motion are solved for this case. The motion integral connected with the energy conservation law and the form of the corresponding operator, its eigenvalues and eigenfunctions are found. The exact solutions of the Schrodinger equation is obtained and the correspondence with the classical problem is investigated. 
@article{TMF_1975_22_1_a7,
     author = {I. R. Svin'in},
     title = {Quantum-mechanical description of friction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_22_1_a7/}
}
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I. R. Svin'in. Quantum-mechanical description of friction. Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 1, pp. 97-108. http://geodesic.mathdoc.fr/item/TMF_1975_22_1_a7/