Spectral theory of ordinary differential operators
Spectral theory of ordinary differential operators
Eigenvalues in gaps of perturbed periodic Dirac operators: numerical evidence
Journal of Computational and Applied Mathematics - On the occasion of the 65th birthday of Prof. Michael Eastham
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It was recently shown that the point spectrum of the separated Coulomb-Dirac operator H0(k) is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment Ha(k) as the anomaly parameter tends to 0; this spectral stability holds for all Coulomb coupling constants c for which H0(k) has a distinguished self-adjoint extension if the angular momentum quantum number k is negative, but for positive k there are certain exceptional values for c. Here we obtain an explicit formula for these exceptional values. In particular, it implies spectral stability for the three-dimensional Coulomb-Dirac operator if |c|