an:06471583
Zbl 1318.94027
Aptekarev, A. I.; Dehesa, J. S.; S??nchez-Moreno, P.; Tulyakov, D. N.
Asymptotics of \(L_p\)-norms of Hermite polynomials and R??nyi entropy of Rydberg oscillator states
EN
Arves??, Jorge (ed.) et al., Recent advances in orthogonal polynomials, special functions, and their applications. 11th international symposium, Universidad Carlos III de Madrid, Legan??s, Spain, August 29 -- September 2, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-6896-6/pbk). Contemporary Mathematics 578, 19-29 (2012).
2012
a
94A17 11B37 33C45 42C05
Hermite polynomials; R??nyi entropy; Rydberg oscillator states; Hermite polynomials
Summary: The asymptotics of the weighted \(L_{p}\)-norms of Hermite polynomials, which describes the R??nyi entropy of order \(p\) of the associated quantum oscillator probability density, is determined for \(n\to\infty\) and \(p>0\). Then, it is applied to the calculation of the R??nyi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator.
For the entire collection see [Zbl 1250.00015].