论文标题
$ \ mathfrak {l} _ {q} $的参数和$ q $渐近学 - 超几何正交多项式的规范
Parameter and $q$ asymptotics of $\mathfrak{L}_{q}$-norms of hypergeometric orthogonal polynomials
论文作者
论文摘要
超几何正交多项式（Hermite，Laguerre和Jacobi）的三个规范家族控制大量量子系统的固定状态的物理波形。代数$ \ Mathfrak {l} _ {q} $ - 这些多项式的规范描述了这些系统的许多物理，化学和信息理论属性，例如动力学和Weizsäcker能量，位置和动量期望值，Rényi和Shannon熵以及Cramér-Rao，Fisher-Shannon和LMC的复杂性测量。在这项工作中，我们检查并解决了未加权和加权$ \ Mathfrak {l} _ {Q} $ - 这些正交多元的规范的$ q $ - 杂种和参数渐近学（即，当重量函数的参数趋向于无穷大）。这项研究的激励是由这些代数规范应用于高度激发的Rydberg和高维伪经典状态（振荡器样）和其他量子系统的高度伪型伪造状态以及其他量子系统的谐波系统，以及其他质量质量质量的谐波系统。
The three canonical families of the hypergeometric orthogonal polynomials (Hermite, Laguerre and Jacobi) control the physical wavefunctions of the bound stationary states of a great deal of quantum systems. The algebraic $\mathfrak{L}_{q}$-norms of these polynomials describe many physical, chemical and information-theoretical properties of these systems, such as e.g. the kinetic and Weizsäcker energies, the position and momentum expectation values, the Rényi and Shannon entropies and the Cramér-Rao, the Fisher-Shannon and LMC measures of complexity. In this work we examine, partially review and solve the $q$-asymptotics and the parameter asymptotics (i.e., when the weight function's parameter tends towards infinity) of the unweighted and weighted $\mathfrak{L}_{q}$-norms for these orthogonal polynomials. This study has been motivated by the application of these algebraic norms to the energetic, entropic and complexity-like properties of the highly-excited Rydberg and high-dimensional pseudo-classical states of harmonic (oscillator-like) and Coulomb (hydrogenic) systems, and other quantum systems subject to central potentials of anharmonic type.
