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

摘要

We propose a simple alternative proof of the Wronskian representation formula obtained by Gaillard and Matveev for the trigonometric Darboux-P?schl-Teller (TDPT) potentials. It rests on the use of singular Darboux-B?cklund transformations applied to the free particle system combined to the shape invariance properties of the TDPT.