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 trigonometric Darboux–Pöschl–Teller (TDPT) potentials. It rests on the use of singular Darboux–Bäcklund transformations applied to the free particle system combined to the shape inv...

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Bibliographic Details
Published in:Physics letters. A 2014-05, Vol.378 (26-27), p.1755-1759
Main Author: Grandati, Y.
Format: Article
Language:English
Subjects:
Condensed Matter
Invariance
Materials Science
Physics
Proving
Representations
Rest
Solid state physics
Theorems
Transformations
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Summary:We propose a simple alternative proof of the Wronskian representation formula obtained by Gaillard and Matveev for the trigonometric Darboux–Pöschl–Teller (TDPT) 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 TDPT. •Wronskian representation of TDPT and Bessel potentials.•Simple proof of Gaillard–Matveev theorem.•Regular and singular extensions of the constant potential.•Darboux transformations based on excited states.•Confluent case and Wronskian Rayleigh formula.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2014.03.020