On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We s...

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Detalles Bibliográficos
Autores principales:	Falomir, Horacio Alberto, González Pisani, Pablo Andrés, Vega, Federico Gaspar, Cárcamo, D., Méndez, F., Loewe, M.
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2016
Materias:	Matemática Física Noncommutative phase space Quantum mechanics Spectrum of rotationally invariant hamiltonians
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/99534 https://ri.conicet.gov.ar/11336/54415
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-99534
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Matemática Física Noncommutative phase space Quantum mechanics Spectrum of rotationally invariant hamiltonians
spellingShingle	Matemática Física Noncommutative phase space Quantum mechanics Spectrum of rotationally invariant hamiltonians Falomir, Horacio Alberto González Pisani, Pablo Andrés Vega, Federico Gaspar Cárcamo, D. Méndez, F. Loewe, M. On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
topic_facet	Matemática Física Noncommutative phase space Quantum mechanics Spectrum of rotationally invariant hamiltonians
description	We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras sl (2, ℝ) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
format	Articulo Articulo
author	Falomir, Horacio Alberto González Pisani, Pablo Andrés Vega, Federico Gaspar Cárcamo, D. Méndez, F. Loewe, M.
author_facet	Falomir, Horacio Alberto González Pisani, Pablo Andrés Vega, Federico Gaspar Cárcamo, D. Méndez, F. Loewe, M.
author_sort	Falomir, Horacio Alberto
title	On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_short	On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_full	On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_fullStr	On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_full_unstemmed	On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_sort	on the algebraic structure of rotationally invariant two-dimensional hamiltonians on the noncommutative phase space
publishDate	2016
url	http://sedici.unlp.edu.ar/handle/10915/99534 https://ri.conicet.gov.ar/11336/54415
work_keys_str_mv	AT falomirhoracioalberto onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace AT gonzalezpisanipabloandres onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace AT vegafedericogaspar onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace AT carcamod onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace AT mendezf onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace AT loewem onthealgebraicstructureofrotationallyinvarianttwodimensionalhamiltoniansonthenoncommutativephasespace
bdutipo_str	Repositorios
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On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

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