RT info:eu-repo/semantics/article
T1 The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions
A1 Erman, Fatih
A1 Gadella Urquiza, Manuel
A1 Uncu, Haydar
AB 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.
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40879
UL http://uvadoc.uva.es/handle/10324/40879
LA eng
NO 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.
DS UVaDOC
RD 23-abr-2024