Computational methods for Generalized Sturmians basis

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The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range...

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Detalles Bibliográficos
Autores principales: Mitnik, D.M., Colavecchia, F.D., Gasaneo, G., Randazzo, J.M.
Formato: JOUR
Materias:
Atomic spectra
Continuum spectra
Generalized Sturmian functions
Asymptotic behaviors
Central potentials
Computational linear algebra
Computational routines
Computational technique
Computational time
Dinger equation
Eigenvalues
Finite difference
Fixed parameters
Generalized eigenvalues
Generalized Sturmians
Inner region
Matrix systems
Single processors
Sturmian
Two-point
Eigenvalues and eigenfunctions
Atomic spectroscopy
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00104655_v182_n5_p1145_Mitnik
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00104655_v182_n5_p1145_Mitnik
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spelling todo:paper_00104655_v182_n5_p1145_Mitnik2023-10-03T14:09:08Z Computational methods for Generalized Sturmians basis Mitnik, D.M. Colavecchia, F.D. Gasaneo, G. Randazzo, J.M. Atomic spectra Continuum spectra Generalized Sturmian functions Asymptotic behaviors Atomic spectra Central potentials Computational linear algebra Computational routines Computational technique Computational time Continuum spectra Dinger equation Eigenvalues Finite difference Fixed parameters Generalized eigenvalues Generalized Sturmian functions Generalized Sturmians Inner region Matrix systems Single processors Sturmian Two-point Eigenvalues and eigenfunctions Atomic spectroscopy The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds. © 2011 Elsevier B.V. All rights reserved. Fil:Mitnik, D.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Colavecchia, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gasaneo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00104655_v182_n5_p1145_Mitnik
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Atomic spectra
Continuum spectra
Generalized Sturmian functions
Asymptotic behaviors
Atomic spectra
Central potentials
Computational linear algebra
Computational routines
Computational technique
Computational time
Continuum spectra
Dinger equation
Eigenvalues
Finite difference
Fixed parameters
Generalized eigenvalues
Generalized Sturmian functions
Generalized Sturmians
Inner region
Matrix systems
Single processors
Sturmian
Two-point
Eigenvalues and eigenfunctions
Atomic spectroscopy
spellingShingle Atomic spectra
Continuum spectra
Generalized Sturmian functions
Asymptotic behaviors
Atomic spectra
Central potentials
Computational linear algebra
Computational routines
Computational technique
Computational time
Continuum spectra
Dinger equation
Eigenvalues
Finite difference
Fixed parameters
Generalized eigenvalues
Generalized Sturmian functions
Generalized Sturmians
Inner region
Matrix systems
Single processors
Sturmian
Two-point
Eigenvalues and eigenfunctions
Atomic spectroscopy
Mitnik, D.M.
Colavecchia, F.D.
Gasaneo, G.
Randazzo, J.M.
Computational methods for Generalized Sturmians basis
topic_facet Atomic spectra
Continuum spectra
Generalized Sturmian functions
Asymptotic behaviors
Atomic spectra
Central potentials
Computational linear algebra
Computational routines
Computational technique
Computational time
Continuum spectra
Dinger equation
Eigenvalues
Finite difference
Fixed parameters
Generalized eigenvalues
Generalized Sturmian functions
Generalized Sturmians
Inner region
Matrix systems
Single processors
Sturmian
Two-point
Eigenvalues and eigenfunctions
Atomic spectroscopy
description The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds. © 2011 Elsevier B.V. All rights reserved.
format JOUR
author Mitnik, D.M.
Colavecchia, F.D.
Gasaneo, G.
Randazzo, J.M.
author_facet Mitnik, D.M.
Colavecchia, F.D.
Gasaneo, G.
Randazzo, J.M.
author_sort Mitnik, D.M.
title Computational methods for Generalized Sturmians basis
title_short Computational methods for Generalized Sturmians basis
title_full Computational methods for Generalized Sturmians basis
title_fullStr Computational methods for Generalized Sturmians basis
title_full_unstemmed Computational methods for Generalized Sturmians basis
title_sort computational methods for generalized sturmians basis
url http://hdl.handle.net/20.500.12110/paper_00104655_v182_n5_p1145_Mitnik
work_keys_str_mv AT mitnikdm computationalmethodsforgeneralizedsturmiansbasis
AT colavecchiafd computationalmethodsforgeneralizedsturmiansbasis
AT gasaneog computationalmethodsforgeneralizedsturmiansbasis
AT randazzojm computationalmethodsforgeneralizedsturmiansbasis
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