Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.3, pp.304--312

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 3, pp.304--312

Unexpected Supermodels.
Andreas Ruffing

In this article, interrelations between a special type of superpotentials with dilatative scaling behavior and between q-discretized harmonic oscillators are investigated. It turns out that there is a certain equivalence principle between q-discrete oscillators on the one hand and between selfsimilar supermodels on the other hand. q-discrete oscillators thus contribute to a better understanding of quantum mechanical superpotentials, indeed they can be regarded as unexpected supermodels. The main approach in our context will be the combination of spectral methods on Jackson square integrable functions with a formalization of supersymmetric Hamilton operators. A further new observation is this one: By the outlined methods, one can introduce completely new types of lattices to discretize Schrödinger equations.
Key words: lattice quantum mechanics, Schrödinger operator, superpotentials, supermodels, q-discretized harmonic oscillators.

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