Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/9307
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dc.contributor.authorErman, Fatih-
dc.contributor.authorGadella, Manuel-
dc.contributor.authorUncu, Haydar-
dc.date.accessioned2020-07-25T22:09:23Z-
dc.date.available2020-07-25T22:09:23Z-
dc.date.issued2017-
dc.identifier.issn2470-0010-
dc.identifier.issn2470-0029-
dc.identifier.urihttps://doi.org/10.1103/PhysRevD.95.045004-
dc.identifier.urihttps://hdl.handle.net/11147/9307-
dc.description.abstractIn this paper, we consider the one-dimensional semirelativistic Schrdinger equation for a particle interacting with N Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an N x N matrix, called the principal matrix. This matrix essentially includes all the information about the spectrum of the problem. We study the bound state spectrum by working out the eigenvalues of the principal matrix. With the help of the Feynman-Hellmann theorem, we analyze how the bound state energies change with respect to the parameters in the model. We also prove that there are at most N bound states and explicitly derive the bound state wave function. The bound state problem for the two-center case is particularly investigated. We show that the ground state energy is bounded below, and there exists a selfadjoint Hamiltonian associated with the resolvent formula. Moreover, we prove that the ground state is nondegenerate. The scattering problem for N centers is analyzed by exactly solving the semirelativistic Lippmann-Schwinger equation. The reflection and the transmission coefficients are numerically and asymptotically computed for the two- center case. We observe the so-called threshold anomaly for two symmetrically located centers. The semirelativistic version of the Kronig-Penney model is shortly discussed, and the band gap structure of the spectrum is illustrated. The bound state and scattering problems in the massless case are also discussed. Furthermore, the reflection and the transmission coefficients for the two delta potentials in this particular case are analytically found. Finally, we solve the renormalization group equations and compute the beta function nonperturbatively.en_US
dc.language.isoenen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofPhysical Review Den_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.titleOne-dimensional semirelativistic Hamiltonian with multiple Dirac delta potentialsen_US
dc.typeArticleen_US
dc.authorid0000-0003-0398-2225-
dc.institutionauthorErman, Fatih-
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume95en_US
dc.identifier.issue4en_US
dc.identifier.wosWOS:000394370500011en_US
dc.identifier.scopus2-s2.0-85021079995en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1103/PhysRevD.95.045004-
dc.relation.doi10.1103/PhysRevD.95.045004en_US
dc.coverage.doi10.1103/PhysRevD.95.045004en_US
dc.identifier.wosqualityQ1-
dc.identifier.scopusqualityQ1-
item.languageiso639-1en-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.grantfulltextopen-
item.fulltextWith Fulltext-
item.openairetypeArticle-
crisitem.author.dept04.02. Department of Mathematics-
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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