Abstract Quasi-Exactly Solvable Schrödinger Equations occupy an intermediate place
between exactly-solvable (eg the harmonic oscillator and Coulomb problems, etc.) and non …

Recently developed methods to investigate quantum spin systems are reviewed. These
methods are based on somewhat unconventional applications of the spin coherent state …

We discuss various questions that emerge in connection with the Lie-algebraic deformation
of the CP 1 sigma model in two dimensions. First, we supersymmetrize the original model …

A general classification of linear differential and finite-difference operators possessing a
finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner …

We explore a one parameter ζ ζ-deformation of the quantum-mechanical Sine-Gordon and
Double-Well potentials which we call the Double Sine-Gordon (DSG) and the Tilted Double …

We discuss supersymmetric quantum mechanical models with periodic potentials. The
important new feature is that it is possible for both isospectral potentials to support zero …

Hill's equation has drawn an enormous amount of consideration due to its ubiquity in
applications as well as its structural richness. Of particular importance in the last 20 years is …

We study a planar model of a nonrelativistic electron in periodic magnetic and electric fields
that produce a 1D crystal for two spin components separated by a half-period spacing. We fit …

We present a study of non-relativistic superintegrable systems whose invariants are
quadratic in the momenta. In two dimensions, there exist only two inequivalent classes of …

We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS
hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our …