Abstract
We study possible factorizations of supersymmetric (SUSY) transformations in the one-dimensional quantum mechanics into chains of elementary Darboux transformations with nonsingular coefficients. A classification of irreducible (almost) isospectral transformations and of related SUSY algebras is presented. A detailed analysis of SUSY algebras and isospectral operators is performed for the third-order case. Bibliography: 29 titles.
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