Kumar Kirtee, Prasad Vinod
Department of Physics and Astrophysics, University of Delhi, Delhi, 110007, India.
Department of Physics, Motilal Nehru College, University of Delhi, Delhi, 110021, India.
Sci Rep. 2022 May 6;12(1):7496. doi: 10.1038/s41598-022-10854-0.
We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text], [Formula: see text], and [Formula: see text], respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom's wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms.
我们分别计算了自由和俘获的类里德伯氢原子的位置空间香农熵、动量空间香农熵和总香农熵，即[公式：见原文]、[公式：见原文]和[公式：见原文]。阐述了原子序数Z、主量子数n和能量E对里德伯原子香农熵的影响。据我们所知，首次报道了香农熵随态能量E和主量子数n的标度性质。我们的工作解释了香农熵如何表明波函数的局域化 - 非局域化。还讨论了作为俘获里德伯原子波函数节点数度量的总香农熵。我们展示了为什么基于香农熵的不确定关系对于里德伯原子优于海森堡不确定性原理。
