Asymptotics of Orthogonal-Polynomial Functionals and Shannon Information Entropy of Rydberg Atoms

Abstract

The asymptotics of entropic integrals of Laguerre and Gegenbauer polynomials is used to calculate the Shannon information entropy of Rydberg atoms (i.e. giant atoms of hydrogenic type), which provides a bulky spreading measure of their charge density much more appropriate than the standard deviation or Heisenberg measure. These systems are stepping stones from the quantum to classical worlds. Indeed because of its exaggerated properties, a Rydberg atom is a good laboratory for investigating how quantum and classical physics correspond when the latter involves irregular (chaotic) orbits.