Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM

Details Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM

2011-10-18

arxiv.org/abs/1110.3958v2

Int. J. Mod. Phys. A 26 (2011) 5337-5347

Physics

Mathematical Physics

15 pages, no figure; published version

Scientific paper

A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supersymmetric quantum mechanics is extended to $k$th-order one. The polynomial appearing in the potential denominator and its degree are determined. The first-order differential relations allowing one to obtain the associated exceptional orthogonal polynomials from those arising in a ($k-1$)th-order analysis are established. Some nontrivial identities connecting products of Laguerre polynomials are derived from shape invariance.

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