A short proof of the Gaillard-Matveev theorem based on shape invariance arguments
Abstract
We propose a simple alternative proof of the Wronskian representation formula obtained by Gaillard and Matveev for the trigonometric Darboux-Poschl-Teller (TDPT) potentials. It rests on the use of singular Darboux-Backlund transformations applied to the free particle system combined to the shape invariance properties of the TDPT.