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dc.contributor.authorMas A.en_US
dc.contributor.authorPizzichillo F.en_US
dc.date.accessioned2017-08-03T15:51:55Z
dc.date.available2017-08-03T15:51:55Z
dc.date.issued2017-08-03
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/20.500.11824/714
dc.description.abstractThis note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich, Exner and Seba [Dirac operators with a spherically symmetric $\delta$-shell interaction, J. Math. Phys. 30.12 (1989), 2875-2882] and by Arrizabalaga, Mas and Vega [Shell interactions for Dirac operators, J. Math. Pures et Appl. 102.4 (2014), 617-639] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherJournal of Mathematical Physicsen_US
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.relationES/1PE/SEV-2013-0323en_US
dc.relationES/1PE/MTM2014-53145-Pen_US
dc.relationEUS/BERC/BERC.2014-2017en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectDirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentialsen_US
dc.titleThe relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximationen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US
dc.identifier.doi10.1063/1.5000381


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