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 …

This book introduces the factorization method in quantum mechanics at an advanced level,
with the aim of putting mathematical and physical concepts and techniques like the …

The one-dimensional Schrödinger equation for the potential x 6+ αx 2+ l (l+ 1)/x 2 has many
interesting properties. For certain values of the parameters l and α the equation is in turn …

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the
salient features of supersymmetry are embedded, SCQM (supersymmetric classical and …

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts
and the real shifts is presented in parallel with the corresponding results in the ordinary …

Most textbooks explain quantum mechanics as a story where each step follows naturally
from the one preceding it. However, the development of quantum mechanics was exactly the …

Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of
exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the …

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' …

In a search for pairs of quantum systems linked by dynamical symmetries, we give a
systematic analysis of novel extensions of standard one-dimensional supersymmetric …

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new
potentials with known spectra departing from an initial solvable one. In these lecture notes …