## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 18 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*