TY - RPRT
T1 - Discrete spectra for critical Dirac-Coulomb Hamiltonians
Y1 - 2017
A1 - Matteo Gallone
A1 - Alessandro Michelangeli
AB - 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, Sommerfeldâ€™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 Sommerfeldâ€™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.
UR - http://preprints.sissa.it/handle/1963/35300
U1 - 35606
U2 - Mathematics
U4 - 1
ER -