Dirac Hamiltonian for strong Coulomb fields

Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials

“…Finally, Klaus and Wüst showed in [16] that these self-adjoint extensions coincide. We also cite [4]: in this work, using the partial wave decomposition and the Von Neumann theory, the authors could characterize the distinguished self-adjoint extension by the fact that the energy of the ground state is continuous in ν. In [9], applying the Kreȋn-Višik-Birman extension theory, Gallone and Michelangeli described the self-adjointness of H 0 + V C for ν < 1, in terms of boundary conditions at the origin, and in [10] they determine the discrete spectrum of such extensions.…”

A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator

“…It is well known (see [25]) that H 0 is self-adjoint on H 1 (R 3 ) 4 and essentially self-adjoint on C ∞ c (R 3 ) 4 , moreover σ(H 0 ) = σ ess (H 0 ) = (−∞, −m] ∪ [m, +∞).…”

Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations

“…in other words, one requires that all the functions in the domain of the extension are in the form domain of the potential and the momentum. For details see [6,14,21,23,29,35]. For |ν| ≥ 1 many self-adjoint extensions can be built, and for |ν| > 1 none appears to be distinguished in some suitable sense, see [17,33,36].…”