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Journal of Mathematical Physics / Volume 49 / Issue 8 / QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)

J. Math. Phys. 49, 082104 (2008); http://dx.doi.org/10.1063/1.2968341 (16 pages)

Fisher information of special functions and second-order differential equations

R. J. Yáñez1,2, P. Sánchez-Moreno1,3, A. Zarzo1,4, and J. S. Dehesa1,3

1Instituto Carlos I de Física Teórica y Computacional, University of Granada, 18071, Granada, Spain
2Departamento de Matemática Aplicada, University of Granada, 18071, Granada, Spain
3Departamento de Física Atómica, Molecular y Nuclear, University of Granada, 18071, Granada, Spain
4Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, 18006, Madrid, Spain

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(Received 4 April 2008; accepted 18 July 2008; published online 18 August 2008)

We investigate a basic question of analytic information theory, namely, the evaluation of the Fisher information and the relative Fisher information with respect to a non-negative function, for the probability distributions obtained by squaring the special functions of mathematical physics which are solutions of second-order differential equations. We obtain explicit expressions for these information-theoretic properties via the expectation values of the coefficients of the differential equation. We illustrate our approach for various nonrelativistic D-dimensional wavefunctions and some special functions of physicomathematical interest. Emphasis is made in the Nikiforov–Uvarov hypergeometric-type functions, which include and generalize the Hermite functions and the Gauss and Kummer hypergeometric functions, among others.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FISHER’S INFORMATION OF A PROBABILITY DENSITY
    1. The Fisher information
    2. The relative Fisher information
  3. FISHER’S INFORMATION OF SPECIAL FUNCTIONS FROM THEIR DIFFERENTIAL EQUATIONS
  4. RELATIVE FISHER INFORMATION OF SPECIAL FUNCTIONS
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

differential equations, information theory, quantum theory, wave functions

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2968341

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    M. J. W. Hall, Phys. Rev. A 62, 012107 (2000).

    M. J. W. Hall, Phys. Rev. A 64, 052103 (2001).

    A. Nagy, J. Chem. Phys. 119, 9401 (2003)JCPSA6000119000018009401000001.

    E. Romera, P. Sánchez-Moreno, and J. S. Dehesa, J. Math. Phys. 47, 103504 (2006)JMAPAQ000047000010103504000001.

    E. Romera, J. C. Angulo, and J. S. Dehesa, Phys. Rev. A 59, 4064 (1999).

    E. Romera and J. S. Dehesa, J. Chem. Phys. 120, 8906 (2004)JCPSA6000120000019008906000001.

    J. S. Dehesa, S. López-Rosa, B. Olmos, and R. J. Yáñez, J. Math. Phys. 47, 052104 (2006)JMAPAQ000047000005052104000001.

    E. Romera and J. S. Dehesa, Phys. Rev. A 50, 256 (1994).

    B. R. Frieden, Phys. Rev. A 41, 4265 (1990).

    J. S. Dehesa, S. López-Rosa, and R. J. Yáñez, J. Math. Phys. 48, 043503 (2007)JMAPAQ000048000004043503000001.

    M. Reginatto, Phys. Rev. A 58, 1775 (1998).

    B. R. Frieden, A. Plastino, A. R. Plastino, and B. H. Soffer, Phys. Rev. E 60, 48 (1999).

    W. van Assche, R. J. Yáñez, and J. S. Dehesa, J. Math. Phys. 36, 4106 (1995)JMAPAQ000036000008004106000001.

    W. P. Schleich and J. P. Dahl, Phys. Rev. A 65, 052109 (2002).

    J. S. Dehesa, A. Martínez-Finkelshtein, and V. N. Sorokin, J. Math. Phys. 44, 36 (2003)JMAPAQ000044000001000036000001.


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