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UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
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PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoreticno fiziko

Difference Ladder Operators for a
Harmonic Schrödinger Oscillator
Using Unitary Linear Lattices

Dr. Andreas Ruffing

Technische Universität München, Zentrum Mathematik
Arcisstrasse 21, D-80333 München, Germany

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 $l^{2}({\Bbb{Z}})$ spaces. Eventual applications to mathematical physics and numerical Schrödinger theory are briefly discussed.

Seminarsko predavanje bo v sredo, 13. marca 2002 ob 15:15 uri v se- minarski sobi CAMTP, Krekova 2, pritlicje. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --