An Interdisciplinary Journal

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

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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Last updated: *June 19, 2001*