Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics |
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Authors: | Nicolae Cotfas |
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Institution: | (1) Faculty of Physics, University of Bucharest, PO Box 76-54, Bucharest, Romania |
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Abstract: | A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions. |
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Keywords: | Associated special functions orthogonal polynomials raising/lowering operators Schr?dinger equation |
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