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Quasi-exactly-solvable problems andsl(2) algebra

- A. Turbiner
- Mathematics
- 1 September 1988

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 is… Expand

FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane

- F. Tremblay, A. Turbiner, P. Winternitz
- Mathematics, Physics
- 4 April 2009

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 of… Expand

EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS

- W. Ruhl, A. Turbiner
- Physics, Mathematics
- 16 June 1995

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-body… Expand

Analytic continuation of eigenvalue problems

- C. Bender, A. Turbiner
- Physics
- 22 February 1993

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, analytic… Expand

Lie algebras and polynomials in one variable

- A. Turbiner
- Mathematics
- 21 September 1992

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 on… Expand

Exact solvability of superintegrable systems

- P. Tempesta, A. Turbiner, P. Winternitz
- Physics, Mathematics
- 23 November 2000

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 of… Expand

Periodic orbits for an infinite family of classical superintegrable systems

- F. Tremblay, A. Turbiner, P. Winternitz
- Mathematics, Physics
- 2 October 2009

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. This… Expand

SOLVABILITY OF THE G2 INTEGRABLE SYSTEM

- M. Rosenbaum, A. Turbiner, A. Capella
- Physics, Mathematics
- 7 July 1997

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, for… Expand

QUASI-EXACTLY-SOLVABLE DIFFERENTIAL EQUATIONS

- A. Turbiner
- Physics, Mathematics
- 12 September 1994

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 any… Expand

The Heun operator as a Hamiltonian

- A. Turbiner
- Physics, Mathematics
- 7 March 2016

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 to… Expand

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