A short proof of the Gaillard-Matveev theorem based on shape invariance arguments
classification
🧮 math-ph
math.MPquant-ph
keywords
invarianceproofshapeacklundalternativeappliedargumentscombined
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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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