Exact solution of the Schr?dinger equation with a Lennard–Jones potential

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• 作者：J. Sesma (1)
  
• 关键词：Schr?dinger equation ; Lennard–Jones potential ; Floquet solutions ; Thomé solutions ; Bound states ; 34B09 ; 34B60 ; 34M40 ; 81Q05 ; 81V45
• 刊名：Journal of Mathematical Chemistry
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：51
• 期：7
• 页码：1881-1896
• 全文大小：227KB
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• 作者单位：J. Sesma (1)
  
  1. Departamento de Física Teórica, Universidad de Zaragoza, 50009, Saragossa, Spain
  

文摘

The Schr?dinger equation with a Lennard–Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given.