Summary
From the point of view of quantum mechanics, the problem of two coupled oscillators with two different coupling parameters is considered. By using the accurate definition of Dirac operators the wave function in both coherent state and number state (Schrödinger picture) are obtained. The Green's function and the expectation value of the energy are calculated; the transition amplitude between the coherent states when the coupling parameters are different and equal, as well as the eigenstates, are given. The constants of the motion for such a system have been also considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. R. Mollow andR. J. Glauber:Phys. Rev.,16, 1076 (1967).
W. H. Louisell, A. Yariv andA. E. Siegman:Phys. Rev.,124, 1646 (1961).
J. Tucker andD. F. Walls:Ann. Phys. (N. Y.),52, 1 (1969).
J. Tucker andD. F. Walls:Phys. Rev.,178, 2036 (1969).
E. Y. C. Lu:Phys. Rev. A,8, 1053 (1973).
M. S. Abdalla:Phys. Rev. A,35, 4160 (1987).
M. S. Abdalla, R. K. Colegrave andA. A. Selim:Physica A,151, 467 (1988).
M. S. Abdalla:Physica A,162, 241 (1990)
M. S. Abdalla andS. S. Hassan:Physica A,163, 822 (1990).
M. S. Abdalla:Phys. Rev. A,41, 3775 (1990).
M. S. Abdalla:Physica A,179, 131 (1991).
E. A. Mishkin andD. F. Walls:Phys. Rev.,185, 1618 (1969).
D. F. Walls andR. Barakat:Phys. Rev. A,1, 446 (1970).
G. P. Agrawal andC. L. Mehta:J. Phys. A,7, 607 (1974).
B. Yurke, W. Schleich andD. F. Walls:Phys. Rev. A,42, 1703 (1990).
M. S. Abdalla:J. Mod. Optics,39, 771 (1993);39, 1067 (1993).
H. R. Lewis andW. B. Riesenfeld:J. Math. Phys.,10, 1458 (1968).
R. K. Colegrave andM. S. Abdalla:J. Phys. A,16, 3805 (1983).
R. K. Colegrave, M. S. Abdalla andM. A. Mannan:J. Phys. A,17, 1567 (1984);R. K. Colegrave andM. A. Mannan:J. Math. Phys. 29, 1580 (1988) and references therein.
H. P. Yuen:Phys. Rev. A,13, 2226 (1976).
M. S. Abdalla:Physica A,202, 301 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abdalla, M.S. Quantum mechanics of two coupled oscillators. Nuovo Cim B 109, 443–457 (1994). https://doi.org/10.1007/BF02728385
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02728385