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

JOHN WILEY & SONS INC

Año: 2007 vol. 107 p. 832 - 844

0020-7608

In this work we introduce a method to construct Sturmian functions for general interaction potentials 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 re-written for these expansions and completeness achieved throughincreasing the basis size. We apply the method to the Coulomb and Herman & 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.