Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials
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In this paper, all quantal systems related to the exceptional Laguerre and Jacobi polynomials can be constructed in a direct and systematic way, without the need of shape invariance and Darboux-Crum transformation.Abstract:
We show how all the quantal systems related to the exceptional Laguerre and Jacobi polynomials can be constructed in a direct and systematic way, without the need of shape invariance and Darboux-Crum transformation. Furthermore, the prepotential need not be assumed a priori. The prepotential, the deforming function, the potential, the eigenfunctions and eigenvalues are all derived within the same framework. The exceptional polynomials are expressible as a bilinear combination of a deformation function and its derivative. Subject Index: 010, 064read more
Citations
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Higher-order susy, exactly solvable potentials, and exceptional orthogonal polynomials
TL;DR: In this article, 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.
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Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials
TL;DR: In this paper, exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of $k$th-order supersymmetric quantum mechanics, with special emphasis on $k=2.
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TL;DR: In this paper, the type III Hermite Xm exceptional orthogonal polynomial family is generalized to a double-indexed one and corresponding rational extensions of the harmonic oscillator are constructed by using second-order supersymmetric quantum mechanics.
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References
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An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
TL;DR: In this article, two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem are presented, and they are shown to be orthogonal with respect to a positive definite inner product defined over the compact interval [ − 1, 1 ] or the half-line [ 0, ∞ ), respectively.
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