Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices

Authors:
Andreas Ruffing;Julian Lorenz;Konstantin Ziegler
Affiliations:
Department of Mathematics, Munich University of Technology, Boltzmannstrasse 3, D-85747 Garching, Germany;Department of Mathematics, Munich University of Technology, Boltzmannstrasse 3, D-85747 Garching, Germany;Department of Mathematics, Munich University of Technology, Boltzmannstrasse 3, D-85747 Garching, Germany
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

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Abstract

The formalism of raising and lowering operators is developed for the difference operator analogue of a quantum harmonic oscillator which acts on functions on a discrete support. The grid under consideration is a mixed version of an equidistant lattice and a q-linear grid. Several properties of the grid are described. The grids under consideration are referred to by the name unitary linear lattices. The ladder difference operators are derived and compared with the continuum situation. The arising spectral problems for these operators are dealt by using the theory of bilateral Jacobi operators in weighted l2(Z) spaces. Eventual applications to mathematical physics and numerical Schrödinger theory are briefly discussed.