Physics – Mathematical Physics
Scientific paper
2009-03-16
Journal of Mathematical Sciences, 151, No. 2 (2008) 2924-2936
Physics
Mathematical Physics
13 pages
Scientific paper
In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux - Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures on reducibility of differential operators for spectral equivalence transformations. Analysis of the general case is performed with all the necessary proofs.
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