Abstract
In view of the description of classical systems using the notion of the wave function of the classical systems suggested in our previous publications, we consider a classical parametric oscillator both in the Hilbert-space representation and the tomographic-probability representation. The time-dependent integrals of motion and Gaussian solutions of the Liouville kinetic equation for the classical-oscillator’s tomograms are found in an explicit form. The Fock states of the classical parametric oscillator and the propagator are studied in the tomographic representation.
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References
V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 28, 535 (2007).
Olga V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 18, 407 (1997).
S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
V. I. Man’ko and O. V. Man’ko, Phys. At. Nucl., 69, 1085 (2006).
V. P. Ermakov, Univ. Izv. Kiev., 20, 1 (1880).
K. Husimi, Prog. Theor. Phys., 9, 381 (1953).
K. Husimi, Prog. Theor. Phys. 9, 238 (1953).
H. R. Lewis Jr. and W. B. Riesenfeld, J. Math. Phys, 10, 1458 (1969).
I. A. Malkin, V. I. Man’ko, and D. A. Trifonov, Phys. Let. A, 30, 414 (1969).
I. A. Malkin, V. I. Man’ko, and D. A. Trifonov, Phys. Rev. D, 2, 1371 (1970).
I. A. Malkin and V. I. Man’ko, Phys. Let. A, 32, 243 (1970).
V. V. Dodonov, I. A. Malkin, and V. I. Man’ko, Physica, 59, 241 (1972).
V. V. Dodonov and A. V. Dodonov, J. Russ. Laser Res., 26, 445 (2005).
V. V. Dodonov, A. B. Klimov, and V. I. Man’ko, Phys. Let. A, 142, 511 (1989).
J. Schwinger, Proc. Natl. Acad. Sci. USA, 89, 4091 (1992).
J. Radon, Ber. Sachs. Akad. Wiss., Leipzig, 69, 262 (1917).
H. Weyl, Z. Phys., 46, 1 (1928).
E. Wigner, Phys. Rev., 40, 749 (1932).
J. E. Moyal, Proc. Cambridge Philos. Soc., 45, 99 (1949).
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Chernega, V.N., Man’ko, V.I. The wave function of the classical parametric oscillator and the tomographic probability of the oscillator’s state. J Russ Laser Res 29, 347–356 (2008). https://doi.org/10.1007/s10946-008-9024-3
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DOI: https://doi.org/10.1007/s10946-008-9024-3