Information-theoretic-based spreading measures of orthogonal polynomials
Mathematical Physics
2013-05-17 v1 math.MP
Abstract
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.
Cite
@article{arxiv.1305.3711,
title = {Information-theoretic-based spreading measures of orthogonal polynomials},
author = {Jesus S. Dehesa and A. Guerrero and Pablo Sánchez-Moreno},
journal= {arXiv preprint arXiv:1305.3711},
year = {2013}
}
Comments
17 pages