Dutt-Khare-Varshni Potential and Its Quantized-by-Heun-Polynomials SUSY Partners as Nontrivial Examples of Solvable Potentials Explicitly Expressible in Terms of Elementary Functions

2015/08/11 by Gregory Natanson, G. Natanson, Natanson, G.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1508.04738

51 pages, 2 figures

arxiv created 2015/08/11 · openalex publication_date 2015/08/11 · arxiv updated 2015/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper presents a detailed analysis of the so-called "Double-Root Tangent-Polynomial" (DRtTP) reduction of the regular Gauss-reference (r-GRef) potential exactly solvable by hypergeometric functions. It is shown that the Dutt-Khare-Varshni (DKV) potential represents a remarkable particular case when the DRtTP r-GRef becomes expressible in terms of elementary functions. This is also true for its basic single- or double-step SUSY partners which are either exactly or conditionally exactly quantized by Heun polynomials (Hp-EQ or Hp-CEQ, respectively).

Citations

• Heun-Polynomial Representation of Regular-at-Infinity Solutions for the Basic SUSY Ladder of Hyperbolic Pöschl-Teller Potentials Starting from the Reflectionless Symmetric Potential Well

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• Single-Source Nets of Algebraically-Quantized Reflective Liouville Potentials on the Line I. Almost-Everywhere Holomorphic Solutions of Rational Canonical Sturm-Liouville Equations with Second-Order Poles

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