Regensburg 1998 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 8: Endliche Quantensysteme

MP 8.8: Fachvortrag

Donnerstag, 26. März 1998, 17:00–17:20, H46

Accumulation of Discrete Eigenvalues of the Radial Dirac Operator — •Joseph Lutgen — Universit"at Regensburg, NWF-I Mathematik, D-93040 Regensburg

We investigate accumulation of eigenvalues of a Dirac operator (with spherically symmetric potential) at the endpoints of the gap in the essential spectrum. The Dirac operator is completely reduced by the so-called "partial wave subspaces" which are subspaces of definite angular mometum and definite parity. It is shown that the point spectra of the restrictions of the Dirac operator to these subspaces are equivalent to the point spectra of certain singular Sturm-Liouville problems on the semi-axis whose coefficients depend nonlinearly on the spectral parameter. Sufficient and necessary conditions for accumulation of eigenvalues of these problems at the endpoints of the gap in the essential spectrum are then given.