In the past ten years, the ideas of supersymmetry have been profitably applied to many
nonrelativistic quantum mechanical problems. In particular, there is now a much deeper …

The authors give explicit point canonical transformations which map twelve types of shape
invariant potentials (which are known to be exactly solvable) into two potential classes. The …

Starting from a potential with a continuum of energy eigenstates, we show how the methods
of supersymmetric quantum mechanics can be used to generate families of potentials with …

We discuss in some detail the self-similar potentials of Shabat [Inverse Prob. 8, 303 (1992)]
and Spiridonov [Phys. Rev. Lett. 69, 298 (1992)] which are reflectionless and have an infinite …

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 …

We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via
two-step confluent Darboux transformations. The former are strictly isospectral to the initial …

Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as
solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of …

Based on the Gaussian wave packet solution for the harmonic oscillator and the
corresponding creation and annihilation operators, a generalization is presented that also …

The possibility for the Jacobi equation to admit, in some cases, general solutions that are
polynomials has been recently highlighted by Calogero and Yi, who termed them para …

Darboux transformation is applied to three classical potentials, namely the harmonic
oscillator, effective Coulomb and Morse potentials to generate exactly solvable potentials of …