Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials

We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic deri...

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Detalles Bibliográficos
Autores principales:	Amore, Paolo, Fernández, Francisco Marcelo
Formato:	Articulo Preprint
Lenguaje:	Inglés
Publicado:	2015
Materias:	Física Química Ciencias Exactas Anharmonic oscillator Convergence Finite wells One-dimensional schrödinger equation Small-energy series
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/97260 https://ri.conicet.gov.ar/11336/82153 https://link.springer.com/article/10.1007/s10910-015-0492-8 https://arxiv.org/abs/1410.5813
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-97260
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Física Química Ciencias Exactas Anharmonic oscillator Convergence Finite wells One-dimensional schrödinger equation Small-energy series
spellingShingle	Física Química Ciencias Exactas Anharmonic oscillator Convergence Finite wells One-dimensional schrödinger equation Small-energy series Amore, Paolo Fernández, Francisco Marcelo Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
topic_facet	Física Química Ciencias Exactas Anharmonic oscillator Convergence Finite wells One-dimensional schrödinger equation Small-energy series
description	We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.
format	Articulo Preprint
author	Amore, Paolo Fernández, Francisco Marcelo
author_facet	Amore, Paolo Fernández, Francisco Marcelo
author_sort	Amore, Paolo
title	Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_short	Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_full	Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_fullStr	Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_full_unstemmed	Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_sort	small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
publishDate	2015
url	http://sedici.unlp.edu.ar/handle/10915/97260 https://ri.conicet.gov.ar/11336/82153 https://link.springer.com/article/10.1007/s10910-015-0492-8 https://arxiv.org/abs/1410.5813
work_keys_str_mv	AT amorepaolo smallenergyseriesforonedimensionalquantummechanicalmodelswithnonsymmetricpotentials AT fernandezfranciscomarcelo smallenergyseriesforonedimensionalquantummechanicalmodelswithnonsymmetricpotentials
bdutipo_str	Repositorios
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Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials

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