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Quasi-exactly-solvable problems andsl(2) algebra
Recently discovered quasi-exactly-solvable problems of quantum mechanics are shown to be related to the existence of the finite-dimensional representations of the groupSL(2,Q), whereQ=R, C. It isExpand
FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane
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 separation ofExpand
EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS
Translationally invariant symmetric polynomials as coordinates for N-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland N-bodyExpand
Analytic continuation of eigenvalue problems
In this paper we consider the dependence of Schrodinger equation eigenvalue problems on the coupling-constant parameters in the potential. We show that unless great care is taken, analyticExpand
Lie algebras and polynomials in one variable
A classification of linear differential and difference equations in one variable having polynomial solutions (the generalized Bochner problem) is presented. The idea of the approach is based onExpand
Exact solvability of superintegrable systems
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 their integrals ofExpand
Periodic orbits for an infinite family of classical superintegrable systems
We show that all bounded trajectories in the two-dimensional classical system with the potential are closed for all integer and rational values of k. The period is and does not depend on k. ThisExpand
SOLVABILITY OF THE G2 INTEGRABLE SYSTEM
It is shown that the three-body trigonometric G2 integrable system is exactly solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, forExpand
QUASI-EXACTLY-SOLVABLE DIFFERENTIAL EQUATIONS
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polyno- mial basis is given. The main result is that anyExpand
The Heun operator as a Hamiltonian
It is shown that the celebrated Heun operator + is the Hamiltonian of the -quantum Euler–Arnold top of spin ν in a constant magnetic field. For it is canonically equivalent toExpand
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