Klein's paradox and the relativistic d-shell interaction in R3
Under certain hypotheses of smallness on the regular potential V, we prove that the Dirac operator in Unexpected text node: 'R', coupled with a suitable rescaling of V, converges in the strong resolvent sense to the Hamiltonian coupled with a Unexpected text node: 'd'-shell poten...
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| Tipo de documento: | artigo |
| Data de publicação: | 2017 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/169311 |
| Acesso em linha: | https://hdl.handle.net/2117/169311 https://dx.doi.org/10.2140/apde.2018.11.705 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Quantum theory Dirac operator Klein's paradox d-shell interaction Singular integral operator Approximation by scaled regular potentials Strong resolvent convergence Quàntums, Teoria dels Classificació AMS::81 Quantum theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | Under certain hypotheses of smallness on the regular potential V, we prove that the Dirac operator in Unexpected text node: 'R', coupled with a suitable rescaling of V, converges in the strong resolvent sense to the Hamiltonian coupled with a Unexpected text node: 'd'-shell potential supported on Unexpected text node: 'S', a bounded Unexpected text node: 'C' surface. Nevertheless, the coupling constant depends nonlinearly on the potential V; Klein’s paradox comes into play. |
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