Sunday, May 19, 2013

1305.3711 (Jesus S. Dehesa et al.)

Information-theoretic-based spreading measures of orthogonal polynomials    [PDF]

Jesus S. Dehesa, A. Guerrero, Pablo Sánchez-Moreno
The macroscopic properties of a quantum system strongly depend on the spreading of the physical eigenfunctions (wavefunctions) of its Hamiltonian operador over its confined domain. The wavefunctions are often controlled by classical or hypergeometric-type orthogonal polynomials (Hermite, Laguerre and Jacobi). Here we discuss the spreading of these polynomials over its orthogonality interval by means of various information-theoretic quantities which grasp some facets of the polynomial distribution not yet analyzed. We consider the information-theoretic lengths closely related to the Fisher information and R\'enyi and Shannon entropies, which quantify the polynomial spreading far beyond the celebrated standard deviation.
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