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

Abstract

We determine explicitly a boundary triple for the Dirac operator $H:=-i\alpha \cdot \nabla +m\beta +\mathbb{V}(x)$ in ${\mathbb{R}}^3$, for $m\in \mathbb{R}$ and $\mathbb{V}(x)=|x{|}^{-1}(\nu {\mathbb{I}}_4+\mu \beta -i\lambda \alpha \cdot x/|x|\beta )$, with $\nu ,\mu ,\lambda \in \mathbb{R}$. Consequently we determine all the self-adjoint realizations of $H$ in terms of the behaviour of the functions of their domain in the origin. When ${\sup }_x|x||\mathbb{V}(x)|\le 1$, we discuss the problem of selecting the distinguished extension requiring that its domain is included in the domain of the appropriate quadratic form.

References in corpus (10)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Dirac Hamiltonian with superstrong Coulomb field
• Self-adjointness of Dirac operators via Hardy-Dirac inequalities
• Resolvents of self-adjoint extensions with mixed boundary conditions
• Self-adjoint extensions of Dirac operators with Coulomb type singularity
• Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei
• Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
• Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities
• Self-adjoint extensions and unitary operators on the boundary
• Self-Adjoint Extensions of Dirac Operator with Coulomb Potential

Cited by in corpus (2)

• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors