Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 179, Issue 1-2, Pages 185-194Publisher
ELSEVIER
DOI: 10.1016/j.cam.2004.09.040
Keywords
special functions; classical orthogonal polynomials; information theory; Fisher information; Shannon entropy; hydrogenic systems
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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. (c) 2004 Elsevier B.V. All rights reserved.
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