Discrete spectra for critical Dirac-Coulomb Hamiltonians

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dc.contributor.areaMathematicsen_US
dc.contributor.authorGallone, Matteo
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2017-11-06T14:27:38Z
dc.date.available2017-11-06T14:27:38Z
dc.date.issued2017
dc.description.abstractThe one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld’s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld’s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35300
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;44/2017/MATE
dc.relation.lastpage20en_US
dc.subjectDirac-Coulomb operatoren_US
dc.subjectself-adjoint extension theoriesen_US
dc.subjectconfluent hypergeometric equationen_US
dc.subjectsupersymmetric Quantum Mechanicsen_US
dc.titleDiscrete spectra for critical Dirac-Coulomb Hamiltoniansen_US
dc.typePreprinten_US
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