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The effect of singular potentials on the harmonic oscillator |
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| Authors: | C. Filgueiras W. Oliveira |
| Affiliation: | a Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900 João Pessoa, PB, Brazil b International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário Lagoa Nova, 59.072-970 Natal, RN, Brazil c Departamento de Física, Universidade Federal de Juiz de Fora, 36.036-330 Juiz de Fora, MG, Brazil |
| Abstract: | We address the problem of a quantum particle moving under interactions presenting singularities. The self-adjoint extension approach is used to guarantee that the Hamiltonian is self-adjoint and to fix the choice of boundary conditions. We specifically look at the harmonic oscillator added of either a δ-function potential or a Coulomb potential (which is singular at the origin). The results are applied to Landau levels in the presence of a topological defect, the Calogero model and to the quantum motion on the noncommutative plane. |
| Keywords: | Self-adjoint extension Harmonic oscillator Landau levels Calogero model Noncommutative plane |
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