The theory of extensions and explicitly-soluble models Page 1 Russian Mathematical
Surveys The theory of extensions and explicitly-soluble models To cite this article: BS …

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum
mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is …

The progress of the factorization method since the 1935 work of Dirac is briefly reviewed.
Though linked with older mathematical theories the factorization seems an autonomous' …

AA Andrianov, NV Borisov, MV Ioffe, “Factorization method and Darboux transformation for
multidimensional Hamiltonians”, TMF, 61:2 (1984), 183–198; Theoret. and Math. Phys., 61:2 …

A nonlinear (polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-
planned spectral properties is reviewed. The full classification of ladder-reducible and …

A new form to construct complex superpotentials that produce real energy spectra in
supersymmetric quantum mechanics is presented. This is based on the relation between the …

We study the nonlinear (polynomial, N-fold,…) supersymmetry algebra in one-dimensional
QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation …

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a
particular element of the transformation group on the set of Riccati equations considered by …

In this study, we investigate the stationary states of the Glauber-Fock oscillator waveguide
array. We begin by transforming the associated Hamiltonian into the form of a quantum …

A polynomial generalization of supersymmetry in quantum mechanics in one and two
dimensions is proposed. Polynomial superalgebras in one dimension are classified. In two …