A short proof of the Gaillard-Matveev theorem based on shape invariance arguments
Yves Grandati (FCN)
TL;DR
This paper presents a straightforward alternative proof of the Gaillard-Matveev theorem for Darboux-Pöschl-Teller potentials, utilizing shape invariance and Darboux-Bäcklund transformations to simplify the derivation.
Contribution
It introduces a novel, simplified proof method based on shape invariance, enhancing understanding of the Wronskian representation for DPT potentials.
Findings
Simplified proof of the Gaillard-Matveev theorem
Application of shape invariance in potential analysis
Use of Darboux-Bäcklund transformations for derivations
Abstract
We propose a simple alternative proof of the Wronskian representation formula obtained by Gaillard and Matveev for the Darboux-P\"oschl-Teller (DPT) potentials. It rests on the use of singular Darboux-B\"acklund transformations applied to the free particle system combined to the shape invariance properties of the DPT.
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Taxonomy
TopicsNuclear physics research studies · Quantum Mechanics and Non-Hermitian Physics · High-pressure geophysics and materials