SELF-SIMILAR POTENTIALS AND THE Q-OSCILLATOR ALGEBRA AT ROOTS OF UNITY

Properties of the simplest class of self-similar potentials are analyz ed. Wave functions of the corresponding Schrodinger equation provide b ases of representations of the q-deformed Heisenberg-Weyl algebra. Whe n the parameter q is a root of unity, the functional form of the poten tials can be found explicitly. The general q3 = 1 and the particular q 4 = 1 potentials are given by the equi-anharmonic and (pseudo) lemnisc atic Weierstrass functions, respectively.