Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity
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چکیده
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 potentials are given by the equianharmonic and (pseudo)lemniscatic Weierstrass functions respectively. Mathematics Subject Classification (1991). 34L40, 17B37, 33D80, 81R50 To appear in shortened form in Lett.Math.Phys. 27 (1993) On leave from the Moscow Institute of Physics and Technology, Moscow, Russia On leave from the Institute for Nuclear Research, Moscow, Russia International NSERC Fellow
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تاریخ انتشار 1993