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Paper detail

Information-theoretic-based spreading measures of orthogonal polynomials

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 Rényi and Shannon entropies, which quantify the polynomial spreading far beyond the celebrated standard deviation.

preprint2013arXivOpen access
Jesus S. DehesaA. GuerreroPablo Sánchez-Moreno
math-phmath.MP
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Jesus S. DehesaA. GuerreroPablo Sánchez-Moreno

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