The theory of matrix models is reviewed from the point of view of its relation to integrable
hierarchies. Discrete 1-matrix, 2-matrix,'conformal'(multicomponent) and Kontsevich models …

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

Exactly solvable models, that is, models with explicitly and completely diagonalizable
Hamiltonians are too few in number and insufficiently diverse to meet the requirements of …

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials is
introduced. Heretofore, it was believed that the lowest-degree one-dimensional quasi …

It is shown that all four superintegrable quantum systems on the Euclidean plane possess
the same underlying hidden algebra $ sl (3) $. The gauge-rotated Hamiltonians, as well as …

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

We completely determine necessary and sufficient conditions for the normalizability of the
wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable …

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

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 …

A new version of the δ expansion is presented, which, unlike the conventional δ expansion,
can be used to do nonperturbative calculations in a self-interacting scalar quantum field …