Abstract
The nonlinear equation of dissipative quantum mechanics is considered in the relaxation-time approximation. It is shown that the steady current-free state does not change when dissipation is taken into account; in particular, there is no ground-state damping, and the zero energy is conserved. A solution is obtained to the problem of the excitation of a harmonic oscillator, serving as a model of single-mode radiation in an open resonator; the solution obtained describes the evolution of the oscillator from an arbitrary steady state under the action of a constraining force. Transition probabilities between the oscillator steady states are calculated. The results are found to be in agreement with the classical theory of damping oscillations.
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Literature cited
E. Kanai, Prog. Theor. Phys.,3, 440 (1948).
W. E. Brittin, Phys. Rev.,77, 396 (1950).
V. H. Myers, Am. J. Phys.,27, 507 (1959).
E. H. Kerner, Can. J. Phys.,36, 371 (1958).
K. W. H. Stevens, Proc. Phys. Soc.,72, 1027 (1958).
I. R. Svin'in, Teor. Mat. Fiz.,22, 97 (1975).
I. R. Svin'in, Teor. Mat. Fiz.,27, 270 (1976).
I. R. Senitzky, Phys. Rev.,119, 670 (1960).
F. T. Arecchi et al., Quantum Fluctuations of Laser Radiation [Russian translation], Mir, Moscow (1974).
V. S. Mashkevich, Kinetic Theory of Lasers [in Russian], Nauka, Moscow (1971).
R. A. Volkov and N. G. Mamedov, Materials of an All-Union Conference on the Physics of Dielectrics and the Prospects for Its Development [in Russian], LPI, Leningrad (1973), p. 54.
R. A. Volkov, Collected Works on Problems of Microelectronics, Physicomathematical Series [in Russian], Vol. 9, MIÉT, Moscow (1972), p. 115.
M. D. Kostin, J. Chem. Phys.,57, 3589 (1972).
M. D. Kostin, J. Stat. Phys.,12, 145 (1975).
J. A. Weiner and R. E. Forman, Phys. Rev., B,10, 325 (1974).
K.-K. Kan and J. J. Griffith, Phys. Lett.,50B, 241 (1974).
H. B. Catlen and T. A. Welton, Phys. Rev.,83, 34 (1951).
P. Carruthers and M. M. Nieto, Am. J. Phys.,33, 537 (1965).
R. Glauber, Quantum Optics and Electronics (C. de Witt, ed.), New York (1965).
P. Carruthers and M. M. Nieto, Rev. Mod. Phys.,40, 411 (1968).
K. Husimi, Prog. Theor. Phys.,9, 381 (1953).
A. I. Baz', Ya. B. Zel'dovich, and A. M. Perelomov, Scattering, Reactions, and Decays in Nonrelativistic Quantum Mechanics [in Russian], Nauka, Moscow (1971).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–105, September, 1978.
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Bekshaev, A.Y., Volkov, R.A. Quantum theory of a dissipative oscillator. Soviet Physics Journal 21, 1192–1197 (1978). https://doi.org/10.1007/BF00894573
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DOI: https://doi.org/10.1007/BF00894573