A quantum-mechanical anharmonic oscillator with a most interesting spectrum

We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E<sub>0</sub> = 1 is independent of λ. This solution is valid on...

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Detalles Bibliográficos
Autores principales:	Amore, Paolo, Fernández, Francisco Marcelo
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2017
Materias:	Ciencias Exactas Química anharmonic oscillator quasi-exactly solvable perturbation theory Padé summation avoided crossings
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/109370 https://www.sciencedirect.com/science/article/abs/pii/S0003491617301963
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-109370
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Ciencias Exactas Química anharmonic oscillator quasi-exactly solvable perturbation theory Padé summation avoided crossings
spellingShingle	Ciencias Exactas Química anharmonic oscillator quasi-exactly solvable perturbation theory Padé summation avoided crossings Amore, Paolo Fernández, Francisco Marcelo A quantum-mechanical anharmonic oscillator with a most interesting spectrum
topic_facet	Ciencias Exactas Química anharmonic oscillator quasi-exactly solvable perturbation theory Padé summation avoided crossings
description	We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E<sub>0</sub> = 1 is independent of λ. This solution is valid only for λ > 0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ > 0. When λ < 0 the spectrum exhibits an infinite number of avoided crossings at each of which the eigenfunctions undergo dramatic changes in their spatial distribution that we analyse by means of the expectation values ⟨x<sup>2</sup>⟩.
format	Articulo Articulo
author	Amore, Paolo Fernández, Francisco Marcelo
author_facet	Amore, Paolo Fernández, Francisco Marcelo
author_sort	Amore, Paolo
title	A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_short	A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_full	A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_fullStr	A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_full_unstemmed	A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_sort	quantum-mechanical anharmonic oscillator with a most interesting spectrum
publishDate	2017
url	http://sedici.unlp.edu.ar/handle/10915/109370 https://www.sciencedirect.com/science/article/abs/pii/S0003491617301963
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bdutipo_str	Repositorios
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A quantum-mechanical anharmonic oscillator with a most interesting spectrum

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