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 q3 = 1 and the particular q4 = 1… (More)

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