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Higher-order susy, exactly solvable potentials, and exceptional orthogonal polynomials

par Quesne, Christiane
Référence Modern physics letters A, 26, 25, page (1843-1852)
Publication Publié, 2011-08

Article révisé par les pairs

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Résumé :

Exactly solvable rationally-extended radial oscillator potentials, whose wave functions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of kth-order supersymmetric quantum mechanics, with special emphasis on k = 2. It is shown that for μ = 1, 2, and 3, there exist exactly μ distinct potentials of μth type and associated families of exceptional orthogonal polynomials, where μ denotes the degree of the polynomial gμ arising in the denominator of the potentials. © 2011 World Scientific Publishing Company.