### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 001, 13 pages      arXiv:1505.06274      https://doi.org/10.3842/SIGMA.2017.001

### 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 and 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

Received November 23, 2016, in final form December 30, 2016; Published online January 05, 2017

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.

Key words: non-relativistic hydrogen atom; method of brackets; hypergeometric function; associated Laguerre functions.

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