FACTORIZATION OF NONLINEAR SUPERSYMMETRY IN ONE-DIMENSIONAL QUANTUM MECHANICS. I: GENERAL CLASSIFICATION OF REDUCIBILITY AND ANALYSIS OF THE THIRD-ORDER ALGEBRA

摘要

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.