Discrete spectra for critical Dirac-Coulomb Hamiltonians

Abstract

The 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.

24 pages, 3 figures. Version published on Journal of Mathematical Physics (2018)

References in corpus (6)

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Cited by in corpus (8)

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• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
• Two dimensional NLS ground states with attractive Coulomb potential and point interaction
• Mass-ratio condition for non-binding of three two-component particles with contact interactions
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations