The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions
We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinge...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão preliminar |
| Data de publicação: | 2019 |
| País: | España |
| Recursos: | Universidad de Valladolid |
| Repositório: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/40879 |
| Acesso em linha: | https://doi.org/10.1007/978-3-030-20087-9_13 http://uvadoc.uva.es/handle/10324/40879 |
| Access Level: | Acceso aberto |
| Resumo: | We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation. |
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