Data di Pubblicazione:
2018
Citazione:
Discrete spectra for critical Dirac-Coulomb Hamiltonians / M. Gallone, A. Michelangeli. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 59:6(2018), pp. 062108.1-062108.19. [10.1063/1.5011305]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
self-adjoint extensions; cut-off potentials; operators; supersymmetry; equation; matrix
Elenco autori:
M. Gallone, A. Michelangeli
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