Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment
Kalf, Hubert ; Schmidt, Karl Michael
arXiv, 0311448 / Harvested from arXiv
Text on arXiv
We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum quantum number kappa, this holds for all Coulomb coupling constants c for which H_0 has a distinguished self-adjoint realisation. For positive kappa, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H_0 and the limits of eigenvalues of H_a appears, accompanied with additional oscillations of the eigenfunctions of H_a very close to the origin.
Publié le : 2003-11-25
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  Mathematics - Classical Analysis and ODEs,  81V45,  34D15, 34L40, 81Q15 
@article{0311448,
     author = {Kalf, Hubert and Schmidt, Karl Michael},
     title = {Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous
  magnetic moment},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0311448}
}

Kalf, Hubert; Schmidt, Karl Michael. Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous
  magnetic moment. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0311448/