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

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).

arXiv comment51 pages, 2 figures

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• Survey of Nodeless Regular Almost-Everywhere Holomorphic Solutions for Exactly Solvable Gauss-Reference Liouville Potentials on the Line I.Subsets of Nodeless Jacobi-Seed Solutions Co-Existent with Discrete Energy Spectrum