A large class of bound-state solutions of the Schrödinger equation via Laplace transform of the confluent hypergeometric equation

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• 作者：P. H. F. Nogueira ; A. S. de Castro ; D. R. M. Pimentel
• 刊名：Journal of Mathematical Chemistry
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：54
• 期：6
• 页码：1287-1295
• 全文大小：391 KB
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897
• 卷排序：54

文摘

It is shown that analytically soluble bound states of the Schrödinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric equation. It is also shown that all closed-form eigenfunctions are expressed in terms of generalized Laguerre polynomials. The generalized Morse potential is used as an illustration.KeywordsMorse potentialSingular potentialLaplace transformConfluent hypergeometric equation