English

Multi-indexed (q-)Racah Polynomials

Mathematical Physics 2015-06-04 v2 High Energy Physics - Theory Classical Analysis and ODEs math.MP Exactly Solvable and Integrable Systems Quantum Physics

Abstract

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of `virtual state' vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the `solutions' of the matrix Schr\"odinger equation with negative `eigenvalues', except for one of the two boundary points.

Keywords

Cite

@article{arxiv.1203.5868,
  title  = {Multi-indexed (q-)Racah Polynomials},
  author = {Satoru Odake and Ryu Sasaki},
  journal= {arXiv preprint arXiv:1203.5868},
  year   = {2015}
}

Comments

29 pages. The type II (q-)Racah polynomials are deleted because they can be obtained from the type I polynomials. To appear in J.Phys.A

R2 v1 2026-06-21T20:40:20.835Z