Asymptotics of $L_p$-norms of Hermite polynomials and Rényi entropy of Rydberg oscillator states

Abstract

The asymptotics of the weighted $L_p$-norms of Hermite polynomials, which describes the Rényi 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 Rényi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator.

11 pages

References in corpus (1)

• Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds

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