On the Darboux transformations and sequences of p-orthogonal polynomials

Rolanía, D. Barrios; García-Ardila, Juan C.; Manrique, Daniel

doi:10.1016/j.amc.2020.125337

Cited by 3 publications

(1 citation statement)

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“…A general overview and a comprehensive discussion of applications is provided in the monographs [5,6]. Recent applications of the Darboux transformation in a variety of contexts concern the derivative Schrödinger equation [7], coherent states for time-dependent quantum oscillators [8], black hole perturbation theory [9], discrete integrable systems [10], the construction of orthogonal polynomial systems [11], among many others. Restricting ourselves to the case of nonrelativistic Quantum Mechanics, the Darboux transformation was found to be the mathematical core of the supersymmetry formalism (SUSY) [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Inverse-root and inverse-root-exponential potentials: Darboux transformations and elementary Darboux partners

Schulze-Halberg¹,

Ishkhanyan²

2020

Phys. Scr.

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The Schrödinger equations for an inverse-root potential and an inverse-root-exponential potential are studied. We derive conditions under which the hypergeometric solutions of the Schrödinger equation degenerate to elementary functions. By means of Darboux transformations we construct new exactly-solvable Schrödinger equations, focusing on bound state solutions and on cases where the transformed potentials are elementary functions.

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