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首页> 外文期刊>Physical Review, A. Atomic, molecular, and optical physics >Generalized position-momentum uncertainty products: Inclusion of moments with negative orderand application to atoms
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Generalized position-momentum uncertainty products: Inclusion of moments with negative orderand application to atoms

机译：广义位置动量不确定性乘积：包含负阶矩的矩及其应用于原子

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摘要

Rigorous and universal relationships among radial expectation values of any D-dimensional quantum-mechanical system are obtained, using Renyi-like position-momentum inequalities in an information-theoretical framework. Although the results are expressed in terms of four moments (two in position space and two in the momentum one), especially interesting are the cases that provide expressions of uncertainty in terms of products (r~a)~(1/a) (p~b)~(1/b), widely considered in the literature, including the famous Heisenberg relationship (r~2) (p~2)≥D~2/4. Improved bounds for these products have recently been provided, but are always restricted to positive orders a,b > 0. The interesting part of this work are the inequalities for negative orders. A study of these relationships is carried out for atomic systems in their ground state. Some results are given in terms of relevant physical quantities, including the kinetic and electron-nucleus attraction energies, the diamagnetic susceptibility, and the height of the peak of the Compton profile, among others.
机译：在信息理论框架下，使用类Renyi类的位置动量不等式，获得了任何D维量子力学系统的径向期望值之间的严格和通用关系。尽管结果用四个矩表示（两个在位置空间中，两个在动量中一个），但特别有趣的是，这些情况以乘积（r〜a）〜（1 / a）（p 〜b）〜（1 / b），在文献中被广泛考虑，包括著名的海森堡关系（r〜2）（p〜2）≥D〜2/4。最近提供了这些产品的改进边界，但始终限于正阶a，b>0。这项工作的有趣部分是负阶的不等式。对处于基态的原子系统进行了这些关系的研究。根据相关的物理量给出了一些结果，包括动能和电子核吸引能，抗磁化率以及康普顿剖面的峰高等。

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