Abstract
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 via their recurrence relations. Within this framework we obtain the special case of an interesting result, proved by Christian Berg in a much larger ge-nerality: The orthogonality measure for q-discrete Hermite polynomials of type II is not uniquely determined on q-exponential lattices.
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Ruffing, A. On Schrödinger-Hermite Operators in Lattice Quantum Mechanics. Letters in Mathematical Physics 47, 197–214 (1999). https://doi.org/10.1023/A:1007586819925
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DOI: https://doi.org/10.1023/A:1007586819925