Abstract
We discussed some aspects of the tomographic-probability representation of quantum mechanics. Using known generic inequalities for Shannon and relative entropies, we obtain some new inequalities for special functions such as Laguerre, Legendre, and two-variable Hermite polynomials.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. V. Dodonov and V. I. Man’ko., Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physics Institute, Nova Science, Commack, N.Y. (1989), Vol. 183.
I. A. Malkin, V. I. Man’ko., Dynamic Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).
C. E. Shannon, Bell System Tech. J., 27, 379 (1948).
C. E. Shannon, Bell System Tech. J., 27, 623 (1948).
S. Kullback and R. A. Leibler, Ann. Math. Stat., 22, 79 (1951).
S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A., 213, 1 (1996).
A. Ibort, V. I. Manko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).
E. Shrödinger, Ann. Phys. Leipzig, 79, 734 (1926).
L. D. Landau, Z. Phys., 45, 430 (1927).
J. von Neumann, Nachr. Ges. Wiss. Göttingen (1927), p. 245.
E. P. Wigner, Phys. Rev., 40, 749 (1932).
K. Husimi, Proc. Phys. Math. Soc. Jpn, 22, 264 (1940).
E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).
R. J. Glauber, Phys. Rev., 131, 2766 (1963).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, “Symplectic entropy,” in: The Third Feynman Festival, J. Phys.: Conf. Ser., 70, 012007 (2007).
M. A. Man’ko, V. I. Man’ko, S. De Nicola, and R. Fedele, Acta Phys. Hung. B, 26, 71 (2006).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Teor. Mat. Fiz., 152, 241 (2007).
M. A. Man’ko, J. Russ. Laser Res., 30, 514 (2009).
M. A. Man’ko, V. I. Man’ko, and R. Vilela Mandes, J. Russ. Laser Res., 27, 507 (2006).
M. A. Man’ko and V. I. Man’ko, Found. Phys. [DOI 10.1007s/10701-009-9403-9].
M. A. Man’ko, “Probability representation and entropic inequalities in quantum mechanics,” Talk at the International Workshop “Nonlinear Physics. Theory and Experiment. VI” (Gallipoli, Lecce, Italy, 23 June – 3 July 2010) [http://www.fisica.unisalento.it/nonlinear6/talks/Manko.pdf].
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, MS (2000).
O. V. Man’ko, “Tomographic representation of quantum mechanics and statistical physics,” in: Foundations of Probability and Physics-5, American Institute of Physics Conference Proceedings, New York (2009), Vol. 1101.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fesenko, P.N., Man’ko, V.I. Tomographic probability and entropic inequalities for special functions. J Russ Laser Res 31, 368–379 (2010). https://doi.org/10.1007/s10946-010-9157-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-010-9157-z