QHJ route to multi-indexed exceptional Laguerre polynomials and corresponding rational potentials

2017/05/22 by Ranjani, S. Sree
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1705.07682

Abstract

A method to construct multi-indexed exceptional Laguerre polynomials using isospectral deformation technique and quantum Hamilton-Jacobi (QHJ) formalism is presented. We construct generalized superpotentials using singularity structure analysis, which lead to rational potentials with multi-indexed polynomials as solutions. We explicitly construct such rational extensions of the radial oscillator and their solutions, which involve exceptional Laguerre orthogonal polynomials having two indices. The exact expressions for the L1, L2 and L3 type polynomials, along with their weight functions are presented. We also discuss the possibility of constructing more rational potentials with interesting solutions.

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