Elements of information theory
Elements of information theory
Quantum information entropies and orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
Computation of the Entropy of Polynomials Orthogonal on an Interval
SIAM Journal on Scientific Computing
Information theoretic inequalities
IEEE Transactions on Information Theory
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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.