Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei
arXiv:1706.00700 · doi:10.1007/s13324-018-0219-7
Abstract
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kre{\uı}n-Višik-Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neumann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the extension, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.
26 pages, corrected some typos and the values of some constants. Final version to appear in Analysis and Mathematical Physics (2018)
References in corpus (3)
Cited by in corpus (14)
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