Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials

Abstract

We describe the self-adjoint realizations of the operator $H:=-i\alpha \cdot \nabla +m\beta +\mathbb{V}(x)$, for $m\in \mathbb{R}$, and $\mathbb{V}(x)=|x{|}^{-1}(\nu {\mathbb{I}}_4+\mu \beta -i\lambda \alpha \cdot x/|x|\beta )$, for $\nu ,\mu ,\lambda \in \mathbb{R}$. We characterize the self-adjointness in terms of the behaviour of the functions of the domain in the origin, exploiting Hardy-type estimates and trace lemmas. Finally, we describe the distinguished extension.

References in corpus (3)

• Dirac Hamiltonian with superstrong Coulomb field
• Self-adjointness of Dirac operators via Hardy-Dirac inequalities
• Self-Adjoint Extensions of Dirac Operator with Coulomb Potential

Cited by in corpus (8)

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• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
• Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors