Information measures of hydrogenic systems, Laguerre polynomials and spherical harmonics

  • Authors:

  • J. S. Dehesa;S. López-Rosa;B. Olmos;R. J. Yáñez

  • Affiliations:

  • Departamento de Física Moderna, Universidad de Granada, 18071-Granada, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain;Departamento de Física Moderna, Universidad de Granada, 18071-Granada, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain;Departamento de Física Moderna, Universidad de Granada, 18071-Granada, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, 18071-Granada, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Sp ...

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
  • Year:
  • 2005

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Abstract

Fisher's information and Shannon's entropy are two complementary information measures of a probability distribution. Here, the probability distributions which characterize the quantum-mechanical states of a hydrogenic system are analyzed by means of these two quantities. These distributions are described in terms of Laguerre polynomials and spherical harmonics, whose characteristics are controlled by the three integer quantum numbers of the corresponding states. We have found the explicit expression for the Fisher information, and a lower bound for the Shannon entropy with the help of an isoperimetric inequality.