An alternative approach to normalizing the Coulomb $$R_{n \ell }(r)$$ radial solutions
IF 1.7
3区 化学
Q3 CHEMISTRY, MULTIDISCIPLINARY
引用次数: 0
Abstract
The normalization of the radial functions \(R_{n \ell }(r)\) for the solution of Schrödinger’s equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Laguerre polynomials. In this paper we show how to effect the normalization directly from the overall form of the solution and the recursion relation for its series part. Our approach should be applicable to similar problems, such as the harmonic oscillator, and can serve to offer students an alternate method of establishing fully-normalized wavefunctions without invoking the properties of special functions.
对库仑 $$R_{n \ell }(r)$$ 径向解进行归一化的另一种方法
库仑势薛定谔方程解的径向函数 \(R_{n \ell }(r)\) 的归一化通常是通过求助于相关拉盖尔多项式的性质来进行的。在本文中，我们展示了如何直接从解的整体形式及其序列部分的递推关系来实现归一化。我们的方法应适用于类似问题，如谐波振荡器，并可为学生提供另一种建立完全归一化波函数的方法，而无需引用特殊函数的性质。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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来源期刊
CiteScore
3.70
自引率
17.60%
发文量
105
审稿时长
6 months
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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