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Discrete sets of many‐body Sturmians
Author(s) -
Randazzo J. M.,
Frapiccini A. L.,
Colavecchia F. D.,
Gasaneo G.
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21686
Subject(s) - discretization , wave function , coulomb , mathematics , function (biology) , basis (linear algebra) , infinity , basis function , set (abstract data type) , quantum , basis set , physics , quantum mechanics , electron , statistical physics , mathematical analysis , computer science , molecule , geometry , evolutionary biology , biology , programming language
Abstract In this work, we present a method to obtain two‐particle Coulomb Sturmians Functions (CSF) with an expansion in a set of L 2 basis functions. In the two‐body case, we recover the exact (discrete) spectrum of the CSFs for negative energies and a discretized approximation for positive ones. Besides, we make use of this method to analyze the two‐independent electron problem as a Generalized Sturmian problem. We propose a discretized version of the wave function in terms of the CSF states, and show that the problem reduces to find numerical coincidences between energy‐dependent eigencharges of the mutually independent one‐electron systems. This expansion methodology includes the continuum information which is lost in the sets used previously in the literature, and is complete when the size of the basis goes to infinity. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009