arXiv subjects
Publications and source records attributed to Hubert Kalf.
G\"unter Hellwig was the author of influential textbooks on PDEs and differential operators of mathematical physics, an enthusiastic and inspiring teacher to generations of engineers, organiser of PDE conferences at Oberwolfach and a pioneer in index theory.
The hitherto unknown author of a citation by Goethe in his History of Colours is identified as J. E. Montucla and the context of Montucla's quotation is discussed.
We consider spectral problems for many-body Dirac operators mentioned by Dereziński in the IAMP News Bulletin of January 2012. In particular, we derive a representation of the Dirac Coulomb operator for a helium-like ion as a matrix operator of order sixteen. We show that it is essentially self-adjoint (under natural restrictions on the coupling constants), that the essential spectrum of its closure is the whole real line and that it has no eigenvalues.
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.