Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions
In this work, we review two methods used to approach singular Hamiltonians in (2 + 1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects,...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2019-11-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2019.00175/full |
| _version_ | 1828163833182552064 |
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| author | Vinicius Salem Vinicius Salem Ramon F. Costa Edilberto O. Silva Fabiano M. Andrade |
| author_facet | Vinicius Salem Vinicius Salem Ramon F. Costa Edilberto O. Silva Fabiano M. Andrade |
| author_sort | Vinicius Salem |
| collection | DOAJ |
| description | In this work, we review two methods used to approach singular Hamiltonians in (2 + 1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects, which are usually modeled by point interactions. In general, it is possible to apply some kind of regularization procedure, as the vanishing of the wave function at the location of the singularity, ensuring that the wave function is square-integrable and then can be associated with a physical state. However, a study based on the self-adjoint extension approach can lead to more general boundary conditions that still gives acceptable physical states. We exemplify the methods by exploring the bound and scattering scenarios of a spin 1/2 charged particle with an anomalous magnetic moment in the Aharonov-Bohm potential in the conical space. |
| first_indexed | 2024-04-12T01:15:27Z |
| format | Article |
| id | doaj.art-731981f8ec214b3ab31fae60c6cef8bf |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-12T01:15:27Z |
| publishDate | 2019-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-731981f8ec214b3ab31fae60c6cef8bf2022-12-22T03:53:59ZengFrontiers Media S.A.Frontiers in Physics2296-424X2019-11-01710.3389/fphy.2019.00175463211Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) DimensionsVinicius Salem0Vinicius Salem1Ramon F. Costa2Edilberto O. Silva3Fabiano M. Andrade4ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, Castelldefels, SpainPrograma de Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, BrazilPrograma de Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, BrazilDepartamento de Física, Universidade Federal do Maranhão, São Luís, BrazilDepartamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa, BrazilIn this work, we review two methods used to approach singular Hamiltonians in (2 + 1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects, which are usually modeled by point interactions. In general, it is possible to apply some kind of regularization procedure, as the vanishing of the wave function at the location of the singularity, ensuring that the wave function is square-integrable and then can be associated with a physical state. However, a study based on the self-adjoint extension approach can lead to more general boundary conditions that still gives acceptable physical states. We exemplify the methods by exploring the bound and scattering scenarios of a spin 1/2 charged particle with an anomalous magnetic moment in the Aharonov-Bohm potential in the conical space.https://www.frontiersin.org/article/10.3389/fphy.2019.00175/fullcurved spaceself-adjoint operatorscatteringbound statesingular Hamiltonian operatorspin |
| spellingShingle | Vinicius Salem Vinicius Salem Ramon F. Costa Edilberto O. Silva Fabiano M. Andrade Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions Frontiers in Physics curved space self-adjoint operator scattering bound state singular Hamiltonian operator spin |
| title | Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions |
| title_full | Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions |
| title_fullStr | Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions |
| title_full_unstemmed | Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions |
| title_short | Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions |
| title_sort | self adjoint extension approach for singular hamiltonians in 2 1 dimensions |
| topic | curved space self-adjoint operator scattering bound state singular Hamiltonian operator spin |
| url | https://www.frontiersin.org/article/10.3389/fphy.2019.00175/full |
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