L2 Discretization of Sturmian Wave Functions for Coulomb-like Potentials

A. L. FRAPICCINI; V. Y. GONZALEZ; J. M. RANDAZZO; F. D. COLAVECCHIA; G. GASANEO

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Año: 2007 vol. 107 p. 832 - 844

0020-7608

In this work we introduce a method to construct Sturmian functions for general interaction potential in two-body problems. We expand these Sturmians on a finite L2 space, using N Laguerre basis functions to obtain a discrete set of eigenvalues for positive and negative energies. Orthogonality and closure relations are thus rewritten for these expansions; completeness is achieved through increasing the basis size. We apply the method to the Coulomb and Herman and Skillman potential. We study the behavior of the functions obtained and their convergence for an overall range of energies. The Sturmian functions are applied to solve the Schrodinger equation for an active electron in a He-like system.