Eur. Phys. J. Plus (2013) 128: 68
https://doi.org/10.1140/epjp/i2013-13068-2

Regular Article

Wronskian representation for confluent supersymmetric transformation chains of arbitrary order

Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA

^* e-mail: axgeschu@iun.edu

Received: 13 April 2013
Accepted: 29 May 2013
Published online: 26 June 2013

Abstract

We prove that iterations of confluent supersymmetric transformations (confluent SUSY chains) in quantum mechanics can be represented through Wronskian determinants. It is further shown that the latter Wronskian representation remains valid, if the SUSY chain is built from arbitrary combinations of confluent and non-confluent subchains. In addition, we obtain an integral representation of generalized eigenfunctions for quantum-mechanical Hamiltonians that proves useful for the application of confluent SUSY chains. Our results generalize former findings for second- and third-order chains.