In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rnyi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics of a modified -norm of the Gegenbauer polynomials which control the wavefunctions of these states in momentum space. The leading term of these entropic quantities is found from first principles, i.e. by means of the Coulomb potential parameters (space dimensionality, the nuclear charge) and the states’s hyperquantum numbers, in a rigorous simple manner. It is shown that they fulfill a logarithmic growth scaling law with the principal hyperquantum number n which characterizes the Rydberg state.

在这项工作中，通过其动量概率密度的Rnyi和Shannon熵，可以量化高氢态（Rydberg）多维氢系统的动量扩散。这些量是从原子和分子物理学到量子技术的众多领域的核心，是通过一种基于改性剂的强渐近性的方法确定的-Gegenbauer多项式的-范数，它控制这些状态在动量空间中的波函数。这些熵量的首要术语是从第一原理中找到的，即以严格的简单方式借助库仑势参数（空间维数，核电荷）和状态的超量子数。结果表明，它们满足了对数增长标度定律，其主要超量子数n表征了Rydberg态。