Harmonic Oscillator SUSY Partners and Evolution Loops

Harmonic Oscillator SUSY Partners and Evolution Loops

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner...

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Main Author: David J. Fernández
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2012-07-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
supersymmetric quantum mechanics
quantum harmonic oscillator
polynomial Heisenberg algebra
geometric phase
Online Access:http://dx.doi.org/10.3842/SIGMA.2012.041
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spelling doaj-7b00af18ec7e4b5a9f635c9f01ef9dc32020-11-25T01:37:11ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-07-018041Harmonic Oscillator SUSY Partners and Evolution LoopsDavid J. FernándezSupersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied. http://dx.doi.org/10.3842/SIGMA.2012.041supersymmetric quantum mechanicsquantum harmonic oscillatorpolynomial Heisenberg algebrageometric phase
collection DOAJ
language English
format Article
sources DOAJ
author David J. Fernández
spellingShingle David J. Fernández
Harmonic Oscillator SUSY Partners and Evolution Loops
Symmetry, Integrability and Geometry: Methods and Applications
supersymmetric quantum mechanics
quantum harmonic oscillator
polynomial Heisenberg algebra
geometric phase
author_facet David J. Fernández
author_sort David J. Fernández
title Harmonic Oscillator SUSY Partners and Evolution Loops
title_short Harmonic Oscillator SUSY Partners and Evolution Loops
title_full Harmonic Oscillator SUSY Partners and Evolution Loops
title_fullStr Harmonic Oscillator SUSY Partners and Evolution Loops
title_full_unstemmed Harmonic Oscillator SUSY Partners and Evolution Loops
title_sort harmonic oscillator susy partners and evolution loops
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2012-07-01
description Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.
topic supersymmetric quantum mechanics
quantum harmonic oscillator
polynomial Heisenberg algebra
geometric phase
url http://dx.doi.org/10.3842/SIGMA.2012.041
work_keys_str_mv AT davidjfernandez harmonicoscillatorsusypartnersandevolutionloops
_version_ 1725059207440367616

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