Mathematical Physics


Single-Source Nets of Algebraically-Quantized Reflective Liouville Potentials on the Line

Authors: Gregory Natanson

The paper presents the uniform technique for constructing SUSY ladders of rational canonical Sturm-Liouville equations (RCSLEs) conditionally exactly quantized by Gauss-seed (GS) Heine polynomials. Each ladder starts from the RCSLE exactly quantized by classical Jacobi, generalized Laguerre or Romanovski-Routh polynomials. We then use its nodeless almost everywhere holomorphic (AEH) solutions formed by the appropriate set of non-orthogonal polynomials to construct multi-step rational SUSY partners of the given Liouville potential on the line. It was proven that eigenfunctions of each RCSLE in the ladder have an AEH form, namely, each eigenfunction can be represented as a weighted polynomial fraction (PFrs), with both numerator and denominator remaining finite at the common singular points of all the RCSLEs in the given ladder. As a result both polynomials satisfy the second-order differential equations of Heine type.

Comments: 48 Pages.

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Submission history

[v1] 2017-04-06 17:43:13

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