Analytical Study of the Forced Harmonic Oscillator with Time Dependent Parameters by Means of the Invariant Dynamical Linear Operator


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Abstract


A general treatment of the quantum forced harmonic oscillator with time dependent mass and frequency is presented. We use the invariant dynamical linear operator method. We analyse the uncertainty principle and obtain the quantum correlation of the forced quantum harmonic oscillator with parameters depending upon time. We prove that these parameters do not depend on the external force. We evaluate the time dependent probability density; we prove that this parameter depends on the external force.
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Keywords


Quantum Forced Harmonic Oscillator; Invariant Dynamical Linear Operator; Schrödinger Equation; Quantum Correlations

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References


H. R. Lewis, Jr., Math. Phys.9, 1976 (1968).

R. K. Colegravee and M. S. Abdalla, J. Phys. A. Math. Gen.16, 3805 (1983).

S. V. Lawande and A.K.Dhara, Phys. Lett. 99A, 353 (1983).

J. M. Cervero and J.Villarroel, J. Phys. A. Math.Gen.17, 2963 (1984).

A. K. Dhara and S. V. Lawande, Phys. Rev.A30, 560(1984).

A. B. Nassar, Phys. Rev.A32, 1862 (1985), J.Math. Phys.27, 755 (1986).

M. S. Abdalla, R. K. Colegrave and A. Khosravi, Nuevo Cimento 93B, 195 (1986).

R. K. Colgrave and M. S. Abdalla, J. Phys. A. Math.Gen.14, 2269 (1981), Ibid.15, 1549 (1982).

P. G. L. Leach, J. Phys. A.Math. Gen.16, 3261 (1983).

M. S. Abdalla and R. K. Colgrave, Phys. Rev. A32, 1958 (1985).

L.T.Willer and J. Vennik, J. Phys. A. Math. Gen.18, 1985 (1985).

A. B. Nassar, J. M. F. Bassalo and P. T. S. Alencar, Phys. Lett. 113A, 365 (1986).

M. S. Abdalla, Phys. Rev. A33, 2870 (1986); Ibid.34, 4598 (1986).

C. I. Um, K. H. Yeon and W. H. Kahng, J. Phys. A. Math. Gen. 20611 (1987).

M. A. Z.Habeeb, J. Phys. A. Math. Gen. 20, 5929 (1987).

C. F. Souza and A. S. Dutra, Phys. Lett. A.123, 297 (1987).

C. P. Natividade, Am. J. Phys. 56, 921 (1988).

R. K.Colegrave and M. S. Abdalla, Optica Acta 28, 495 (1981).

N. A. Lemos and C .P. Natividade, Nuovo Cimento B99, 211(1987); See also B. R. Holstein, Am .J.Phys.57, 714 (1989).

H. R. Lewis Jr. and W. B. Riesenfeld, J. Math. Phys. A10,1458 (1969).

W .H. Lovisell, quantum statistical proprerties of radiation [N.t.Wley) ; 1973, p. 332.

R. W. Hasse. J. Math. Phys.16 (1975) 2005-2011.

V. V. Dodonov and V. I. Man’ko; Phys. Rev. A20 (1979) 550-560.

P. V. Colgrave and M. S. Abdalla, J. Phys. A. Math. Gen; 15 (1982) 1549-1559

H. C. Kim ; M-H Lee; J,Y, J. and J. K. Kim, Phys. Rev. A. 53(6) (19996) 3767-3771.

S. Pepore; P. Winatal; T. Osatacham and U. Robkol, Scientino 32 (2006) 173-179.

R. K. Colgrave and M. S. Abdalla; J. Phys. A. Math ; Gen 1v (1981) 2269-2280.

M. S. Abdalla, Phys. Rev. A 3416 (1986) 4598.

M. S. Abdalla, Phys. Rev. A33 (5) (1986) 2870-2876.

H. R. Lews and W. B. Riesenfeld, J. Math. Phys. 10 (1985) 1458

P. Caldirolaa, Nuovo Cimento 18 (1941) 393, B 77 (1983) 241.

E. Kanai; Prog. Theor. Phys. 3 (1948) 440.

H. Dekker; Phys. Rep.80 (1981)1.

I. A. Pedrosa , A. Rosas, I. Guedes, J .Phys. A. Math .Gen. 38 (2005) 7757.

Alberes Lopes de Lima, Alexandre Rosas, I. A. Pedrosa, Annals of Physics 323 (2008) 2253 - 2264.

J. R. Ray, Phys. Rev. D25, 3417 (1982)

J. G. Hartly and J. R. Ray, Phys. Rev. A24, 2873 (1981)

M. S. Abdalla, Phys. Rev. A33, 2870 (1986), Ibid.34, 4598 (1986).

V. V. Dodonov and V. I. Manko, Phys. Rev. A20, 550, (1979); ”Group-Theoretical Methods in Physics” (Harwood,1985), pp. 591-612.

Alberes Lopes de Lima, Alexandre Rosas, I. A. Pedrosa, Annals of Phys. 323 (2008) 2253-2264.


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