2020-10-20T00:16:29Zhttps://gredos.usal.es/oai/requestoai:gredos.usal.es:10366/1331492020-06-18T14:54:56Zcom_10366_116214com_10366_4512com_10366_3823col_10366_116215
Gadella, M.
Mateos Guilarte, Juan María
Muñoz-Castañeda, Jose María
Nieto, L. M.
2017-05-19T07:12:30Z
2017-05-19T07:12:30Z
2015-09-25
http://hdl.handle.net/10366/133149
https://dx.doi.org/10.1088/1751-8113/49/1/015204
[EN]In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $q\to 0$ on a potential of the type $v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1} \delta'({y})$, when $ u_0$ and $ u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\mathbb R})$. We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the exceptional cases emerging in the study are also described in full detail. It is shown that for the $v_1=\pm 1$, $w_1=\pm 1$ values of the $\delta^\prime$ couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side.
eng
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-NoDerivs 4.0 International
Mathematical physics
Mathematical Physics
High Energy Physics
Theory
Quantum Physics
Two-point one-dimensional δ-δ’ interactions: non-abelian addition law and decoupling limit
info:eu-repo/semantics/article