2026-04-28T19:49:21Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/408792021-06-24T07:22:53Zcom_10324_22154com_10324_954com_10324_894col_10324_22155
UVaDOC
author
Erman, Fatih
author
Gadella Urquiza, Manuel
author
Uncu, Haydar
2020-05-16T12:23:12Z
2020-05-16T12:23:12Z
2019
1. The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions, F. Erman, M. Gadella, and H. Uncu, in S. Kuru, J. Negro and L.M. Nieto (eds.), Integrability, Supersymmetry and Coherent States. A volume in honour of Professor Véronique Hussin. CRM Series in Mathematical Physics (Berlin: Springer, 2019), pp. 309-322.
http://uvadoc.uva.es/handle/10324/40879
10.1007/978-3-030-20087-9_13
309
322
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.
eng
The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions
info:eu-repo/semantics/article
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b3IgaW5jdW1wbGltaWVudG8gZGUgY3VhbHF1aWVyYSBkZSBsYXMgb2JsaWdhY2lvbmVzIGRlcml2YWRhcyBkZWwgQWN1ZXJkbywgcG9yIHZvbHVudGFkIGV4cHJlc2EgZGVsIEF1dG9yCkVuICBwcnVlYmEgZGUgY29uZm9ybWlkYWQsIGxhcyBwYXJ0ZXMgYWNlcHRhbiBlbCBwcmVzZW50ZSBBY3VlcmRvCgoKCgo=
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