Abstract

The Dirac Hamiltonian in one space dimension is investigated under the influence of a potential of the form −γ/|x|. The corresponding (four-parameter) family of all self-adjoint extensions is given and described via the boundary form. The resolvent is calculated and the spectrum is studied. Furthermore, we examine the zero mass case. In the nonrelativistic limit we obtain the four-parameter family of Schrödinger operators with the Coulomb potential.

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