Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity

Details Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity

1993-04-22

arxiv.org/abs/hep-th/9304107v1

Lett.Math.Phys. 28 (1993) 59-74

Physics

High Energy Physics

High Energy Physics - Theory

15 pp, Latex, to appear in Lett.Math.Phys

Scientific paper

10.1007/BF00739567

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schr\"odinger equation provide bases of representations of the $q$-deformed Heisenberg-Weyl algebra. When the parameter $q$ is a root of unity the functional form of the potentials can be found explicitly. The general $q^3=1$ and the particular $q^4=1$ potentials are given by the equianharmonic and (pseudo)lemniscatic Weierstrass functions respectively.

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