The Jaynes–Cummings Model (JCM) has recently been receiving increased attention as
one of the simplest, yet intricately nonlinear, models of quantum physics. Emphasising the …

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 …

A superintegrable system is, roughly speaking, a system that allows more integrals of motion
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …

Recently discovered quasi-exactly-solvable problems of quantum mechanics are shown to
be related to the existence of the finite-dimensional representations of the group SL (2, Q) …

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 …

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

We discuss a new class of spectral problems discovered recently which occupies an
intermediate position between the exactly-solvable problems (like the famous harmonic …

An infinite family of exactly solvable and integrable potentials on a plane is introduced. It is
shown that all already known rational potentials with the above properties allowing …

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 a new class of spectral problems discovered recently which occupies an
intermediate position between the exactly-solvable problems (eg, harmonic oscillator) and …