Hamiltonian self-adjoint extensions for(2+1)-dimensional Dirac particles
We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux Phi = 2 pi kappa/e. The rotational invariance of this configuration implies that the subspaces of definite angular momentum l+1/2 are inv...
| Authors: | ; |
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2001 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/98034 |
| Online Access: | http://hdl.handle.net/11336/98034 |
| Access Level: | Open access |
| Keyword: | Self-adjoint extensions Dirac operator https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Summary: | We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux Phi = 2 pi kappa/e. The rotational invariance of this configuration implies that the subspaces of definite angular momentum l+1/2 are invariant under the action of the Hamiltonian H. We show that, for l different from the integer part of kappa, the restriction of H to these subspaces, H_l is essentially self-adjoint, while for l equal to the integer part of kappa, H_l admits a one-parameter family of self-adjoint extensions (SAE). In the later case, the functions in the domain of H_l are singular (but square-integrable) at the origin, their behavior being dictated by the value of the parameter gamma that identifies the SAE. We also determine the spectrum of the Hamiltonian as a function of kappa and gamma, as well as its closure. |
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