厄米多项式的$L_p$ -模的渐近性和里德堡振子态的Rényi熵
Asymptotics of $L_p$-norms of Hermite polynomials and Rényi entropy of Rydberg oscillator states
摘要：
对$n\to\infty$和$p>0$确定了描述量子振子概率密度的$p$阶Rényi熵的Hermite多项式的加权$L_{p}$ -范数的渐近性.然后，将其应用于各向同性振子高激发（Rydberg）态量子力学几率密度的Rényi熵的计算。
英文摘要：
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.
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