ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: Orthogonal Polynomials Ruffing, Andreas, Technical University of Munich, Arcisstrasse 21, D-80333 Muenchen On Schrödinger-Hermite Operators in Lattice Quantum Mechanics Starting from the q−Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q−discrete Hermite polynomials occur by their recurrence relations. In this framework we obtain an amazing result, discovered by Christian Berg recently by different methods: The orthogonality measure for q−discrete Hermite polynomials of type II is in general not uniquely determined on q−exponential lattices.