Self-similar potentials and theq-oscillator algebra at roots of unity |
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| Authors: | Sergei Skorik Vyacheslav Spiridonov |
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| Institution: | (1) Department of Physics, University of Southern California, 90089-0484 Los Angeles, CA, USA;(2) Laboratoire de Physique Nucléaire, Université de Montréal, CP 6128, succ. A, H3C 3J7 Montréal, Québec, Canada;(3) Present address: Moscow Institute of Physics and Technology, Moscow, Russia;(4) Present address: Institute for Nuclear Research, Moscow, Russia |
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| Abstract: | Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq
3 = 1 and the particularq
4 = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively. |
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| Keywords: | 34L40 17B37 33D80 81R50 |
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