A short proof of the Gaillard-Matveev theorem based on shape invariance arguments

Yves Grandati (1)

1 FCN - Fédération de Chimie de Nancy

We propose a simple alternative proof of the Wronskian representation formula obtained by Gaillard and Matveev for the Darboux-Pöschl-Teller (DPT) potentials. It rests on the use of singular Darboux-Bäcklund transformations applied to the free particle system combined to the shape invariance properties of the DPT.

Mots clés: confluent SUSY QM; Darboux-Pöschl-Teller potentials; Gaillard-Matveev's theorem; Darboux transformations; Wronskians; supersymmetric quantum mechanics

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Yves Grandati. A short proof of the Gaillard-Matveev theorem based on shape invariance arguments. 2012. ⟨hal-00750572⟩