The quantum-mechanical Coulomb propagator in an L2 function representation

Abstract The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Rolf Gersbacher, John T. Broad
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c219527a745f4e418a373e11a2abe5f3
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:c219527a745f4e418a373e11a2abe5f3
record_format	dspace
spelling	oai:doaj.org-article:c219527a745f4e418a373e11a2abe5f32021-12-02T18:14:08ZThe quantum-mechanical Coulomb propagator in an L2 function representation10.1038/s41598-021-96925-02045-2322https://doaj.org/article/c219527a745f4e418a373e11a2abe5f32021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-96925-0https://doaj.org/toc/2045-2322Abstract The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part of the spectrum is extrapolated numerically, while three integration procedures are applied to the continuum part of the oscillating integral: the Gauss–Pollaczek quadrature, the Gauss–Legendre quadrature along the real axis, and a transformation into a contour integral in the complex plane with the subsequent Gauss–Legendre quadrature. Using the contour integral, the Coulomb propagator can be calculated very accurately from an L $$^2$$ 2 basis. Using the three-term recursion relation of the Pollaczek polynomials, an effective algorithm is herein presented to reduce the number of integrations. Numerical results are presented and discussed for all procedures.Rolf GersbacherJohn T. BroadNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Rolf Gersbacher John T. Broad The quantum-mechanical Coulomb propagator in an L2 function representation
description	Abstract The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part of the spectrum is extrapolated numerically, while three integration procedures are applied to the continuum part of the oscillating integral: the Gauss–Pollaczek quadrature, the Gauss–Legendre quadrature along the real axis, and a transformation into a contour integral in the complex plane with the subsequent Gauss–Legendre quadrature. Using the contour integral, the Coulomb propagator can be calculated very accurately from an L $$^2$$ 2 basis. Using the three-term recursion relation of the Pollaczek polynomials, an effective algorithm is herein presented to reduce the number of integrations. Numerical results are presented and discussed for all procedures.
format	article
author	Rolf Gersbacher John T. Broad
author_facet	Rolf Gersbacher John T. Broad
author_sort	Rolf Gersbacher
title	The quantum-mechanical Coulomb propagator in an L2 function representation
title_short	The quantum-mechanical Coulomb propagator in an L2 function representation
title_full	The quantum-mechanical Coulomb propagator in an L2 function representation
title_fullStr	The quantum-mechanical Coulomb propagator in an L2 function representation
title_full_unstemmed	The quantum-mechanical Coulomb propagator in an L2 function representation
title_sort	quantum-mechanical coulomb propagator in an l2 function representation
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/c219527a745f4e418a373e11a2abe5f3
work_keys_str_mv	AT rolfgersbacher thequantummechanicalcoulombpropagatorinanl2functionrepresentation AT johntbroad thequantummechanicalcoulombpropagatorinanl2functionrepresentation AT rolfgersbacher quantummechanicalcoulombpropagatorinanl2functionrepresentation AT johntbroad quantummechanicalcoulombpropagatorinanl2functionrepresentation
_version_	1718378475969052672

The quantum-mechanical Coulomb propagator in an L2 function representation

Ejemplares similares