A short proof of the Gaillard-Matveev theorem based on shape invariance   arguments
  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. 
Yves Grandati (FCN)
math-ph math.MP quant-ph