In the probability representation of quantum mechanics, the eigenvalue problems in Hilbert space appear as *-genvalue equations. We show the possibility of employing the nondegenerate stationary perturbation method in the probability representation of quantum mechanics. The perturbed eigentomograms and the eigenvalues of energy are shown to be computed ab initio in terms of tomographic symbols of the operators involved.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Mancini, V. I. Man’ko, and P. Tombesi, Quantum Semiclass. Opt., 7, 615 (1995).
S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
S. Mancini, V. I. Man’ko, and P. Tombesi, Found. Phys., 27, 801 (1997).
S. Mancini, O. V. Man’ko, V. I. Man’ko, and P. Tombesi, J. Phys. A: Math. Gen., 34, 3461 (2001).
K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).
D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).
D. G. Welsh, W. Vogel, and T. Opatny, in: E. Wolf (ed.), Progress in Optics, Elsevier, Amsterdam (1999), Vol. 39, p. 63.
O. V. Man’ko, V. I. Man’ko, and G. Marmo, Phys. Scr., 62, 446 (2000).
O. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).
V. I. Man’ko, G. Marmo, and P. Vitale, Phys. Lett. A., 334, 1 (2005).
H. Weyl, The Theory of Groups and Quantum Mechanics, Dover (1931).
E. Wigner, Phys. Rev., 40, 749 (1932).
J. E. Moyal, Proc. Cambridge Philos. Soc., 45, 99 (1949).
J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955).
M. B. Bazrafkan, J. Russ. Laser Res., 29, 426 (2008).
V. I. Man’ko, L. Rosa, and P. Vitale, Phys. Rev. A., 57 3291 (1998).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bazrafkan, M.R., Nahvifard, E. Stationary perturbation theory in the probability representation of quantum mechanics. J Russ Laser Res 30, 392–403 (2009). https://doi.org/10.1007/s10946-009-9079-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-009-9079-9