论文标题
多维谐波系统的分散和类似熵的度量。应用于Rydberg州和高维振荡器
Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators
论文作者
论文摘要
通过主体分散度量（径向预期值）和类似熵的量化量（Fisher Information，Shannon和Rényi熵，不平衡，不平衡的量子概率分布）以及其相关的不确定性关系，对量子多维谐波振荡器的固定状态的扩散特性进行了分析讨论。有时通过潜在参数（振荡器强度，尺寸，$ d $）和HyperQuantum Number $ $（N_R，μ_1，μ_2，\ ldots，μ___{D-1}）$明确给出它们。重点放在高度兴奋的Rydberg（高径向高质量$ n_r $，固定$ D $）和高维（高$ D $，固定固定的Hyperquantum数字）状态上。我们已经使用了一种方法论，在该方法论中，描述了扩散量的Laguerre和Gegenbauer多项式的整体函数的理论确定，在某些权重$ \ Mathfrak {Q} _ {Q} $ - quart of orthogogogonogogonogogonogogonogogonogogonogogonogogonogogonogogonogonogogonogogonogonogogonogogonogogonogogogons上都大大依赖代数性属性和渐近性能。
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and Rényi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, $D$) and the hyperquantum numbers $(n_r,μ_1,μ_2,\ldots,μ_{D-1})$ which characterize the state. Emphasis is placed on the highly-excited Rydberg (high radial hyperquantum number $n_r$, fixed $D$) and the high-dimensional (high $D$, fixed hyperquantum numbers) states. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauer polynomials, which describe the spreading quantities, leans heavily on the algebraic properties and asymptotical behavior of some weighted $\mathfrak{L}_{q}$-norms of these orthogonal functions.
