文章基本信息

标题：The intervals of oscillations in the solutions of the radial Schrödinger differential equation
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作者：Qutaibeh D Katatbeh ; Dimitris M Christodoulou ; James Graham-Eagle 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：47
DOI：10.1186/s13662-016-0777-7
语种：English
出版社：Hindawi Publishing Corporation
摘要：We have previously formulated a program for deducing the intervals of oscillations in the solutions of ordinary second-order linear homogeneous differential equations. In this work, we demonstrate how the oscillation-detection program can be carried out for the radial Schrödinger equation when a Coulomb potential is used to describe the hydrogen atom. The method predicts that the oscillation intervals are finite in radius and their sizes are determined uniquely by the two quantum numbers n and ℓ. Numerical integrations using physical boundary conditions at the origin confirm this oscillatory behavior of the radial Coulomb wavefunctions. Two related differential equations due to Kummer and Whittaker and other attractive electrostatic potentials are also discussed in the same context.
关键词：oscillations ; second-order linear differential equations ; analytical theory ; transformations ; Schrödinger differential equation ; Kummer’s differential equation ; Whittaker differential equation