Summary
The coupled parametric quantum oscillators are discussed. The ground, coherent states and integrals of motion for the parametric chain with time-dependent frequencies are constructed. The possibility of controlling in principle the dispersions of coordinates and momenta is suggested. The squeezing coefficients in coherent states are found.
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References
E. Henley andW. Thirring:Elementary Quantum Field Theory (McGraw-Hill Book Company, New York, San Francisco, Toronto, London, 1962).
C. Kittel Introduction to Solid State Physics (New York, N.Y., 1953), 2nd edition.
V. V. Dodonov, V. I. Man’ko andO. V. Man’ko:Proc. Lebedev Phys. Inst.,200, 155 (1990). (in Russsian).
K. H. Yeon, T. F. George andC. I. Um:Propagators for coupled damped harmonic oscillators, accepted inPhys. Rev. A.
K. H. Yeon, C. I. Um, W. H. Kahng andT. F. George:Phys. Rev. A, 38, 6224 (1988).
K. H. Yeon, T. F. George andC. I. Um:Propagators for N coupled damped driven harmonic oscillators, accepted inJ. Chem. Phys.
H. R. Lewis andW. B. Riesenfeld:J. Math. Phys.,10, 1458 (1969).
I. A. Malkin andV. I. Man’ko:Phys. Lett. A,31, 243 (1970).
I. A. Malkin, V. I. Man’ko andD. A. Trifonov:Sov. Phys. JETP,31, 386 (1970)
V. V. Dodonov, I. A. Malkin andV. I. Man’ko:Int. J. Theor. Phys.,14, 37 (1975).
J. R. Klauder:J. Math. Phys.,4, 1055 (1963).
J. R. Klauder:J. Math. Phys.,4, 1058 (1963).
J. R. Klauder:J. Math. Phys.,5, 177 (1964).
J. McKenna andJ. R. Klauder:J. Math. Phys.,5, 878 (1964).
R. J. Glauber:Phys. Rev.,131, 2766 (1963).
E. Schrödinger:Naturwissenschaften,14, 664 (1926).
I. A. Malkin, V. I. Man’ko andD. A. Trifonov:J. Math. Phys.,14, 576 (1973).
V. V. Dodonov, V. I. Man’ko andO. V. Man’ko:Proc. Lebedev Phys. Inst.,191, 171 (1989) (in Russian).
D. A. Trifonov:Phys. Lett. A,48, 165 (1974).
V. V. Dodonov, E. V. Kurmyshev andV. I. Man’ko:Phys. Lett. A 79, 150 (1980).
V. V. Dodonov, E. V. Kurmyshev andV. I. Man’ko: inProocedings of the First International Seminar on Group Theoretical Methods in Physics, edited byM. A. Markov (Nauka, Moscow, 1980), Vol. 1, p. 227.
E. Schrödinger:Ber. Kgl. Akad. Wiss. (Berlin, 1930), p. 296.
H. P. Robertson:Phys. Rev. A,35, 667 (1930).
K. Husimi:Progr. Theor. Phys.,9, 381 (1953).
V. V. Dodonov andV. I. Man’ko:Proc. Lebedev Phys. Inst.,183, 71 (1987), English translation:Invariants and the Evolution of Nonstationary Quantum Systems, edited byM. A. Markov (Nova Science Publishers, New York, N.Y., 1989), p. 103.
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Dodonov, V.V., Man’ko, O.V. & Man’ko, V.I. Squeezing in quantum parametric chain. Nuov Cim B 107, 513–517 (1992). https://doi.org/10.1007/BF02723628
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DOI: https://doi.org/10.1007/BF02723628