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

Abstract

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger 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.

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

References in corpus (1)

• Exactly Solvable Potentials and Quantum Algebras

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