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The Moments of the Hydrogen Atom by the Method of Brackets Ivan Gonzalez a ,
Karen T. Kohl b ,
Igor Kondrashuk c ,
Victor H. Moll d ,
Daniel Salinas e a Instituto de Física y Astronomia, Universidad de Valparaiso, Avda. Gran Bretaña 1111, Valparaiso, Chile b Department of Mathematics, University of Southern Mississippi, Long Beach, MS 39560, USA c Grupo de Matemática Aplicada & Grupo de Física de Altas Energías, Departmento de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Av. Andres Bello 720, Casilla 447, Chillán, Chile d Department of Mathematics, Tulane University, New Orleans, LA 70118, USA e Departamento de Fisica, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaiso, Chile Abstract:
Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral
involving the associated Laguerre function. The method of brackets is used to evaluate the integral in
closed-form and to produce an expression for this average value as a finite sum.
Keywords:
non-relativistic hydrogen atom; method of brackets; hypergeometric function; associated Laguerre functions.
MSC: 33C45 ;
33C20 ;
81V45 Received: November 23, 2016 ; in final form
December 30, 2016 ; Published online
January 5, 2017
Language: English
DOI:
10.3842/SIGMA.2017.001
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