2026-09-14T12:57:14Zhttps://gredos.usal.es/oai/request
oai:gredos.usal.es:10366/1331492025-04-30T20:44:51Zcom_10366_116214com_10366_4512com_10366_3823col_10366_116215
Gestión del Repositorio Documental de la Universidad de Salamanca author Gadella, M. author Mateos Guilarte, Juan María author Muñoz-Castañeda, Jose María author Nieto, Luis Miguel 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 Attribution-NonCommercial-NoDerivs 4.0 International 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 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 URL https://gredos.usal.es/bitstream/10366/133149/1/MPG_Gadella_Two-point.pdf File MD5 aeafae79edddc0bbf6bbd38e5866c09a 676386 application/pdf MPG_Gadella_Two-point.pdf URL https://gredos.usal.es/bitstream/10366/133149/7/MPG_Gadella_Two-point.pdf.txt File MD5 26ad4cebee4cf590fda82a8c20d428d8 52656 text/plain MPG_Gadella_Two-point.pdf.txt