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...
| Autores: | ; ; ; ; ; |
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| Tipo de documento: | Artigo |
| Estado: | Published version |
| Data de publicação: | 2016 |
| País: | Argentina |
| Recursos: | UNLP |
| Repositório: | SEDICI (UNLP) |
| Idioma: | Inglês |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/99534 |
| Acesso em linha: | http://sedici.unlp.edu.ar/handle/10915/99534 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Matemática Física Noncommutative phase space Quantum mechanics Spectrum of rotationally invariant hamiltonians |
| Resumo: | 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. |
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