Approximation of one-dimensional relativistic point interactions by regular potentials revised

Abstract

We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form $1/\epsilon h(x/\epsilon )\otimes B$, where $B$ is a suitable $2\times 2$ matrix. Moreover, we prove that the limit does not depend on the particular choice of $h$ as long as it integrates to a constant value.

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Cited by in corpus (3)

• General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian