From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model
Mathematical Physics
2011-07-19 v2 math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them are characterized by (i) a discrete symmetry of the Hamiltonian, (ii) a number of polynomial eigenfunctions, (iii) a factorization property for eigenfunctions, and admit (iv) the separation of the radial coordinate and, hence, the existence of the 2nd order integral, (v) an algebraic form in invariants of a discrete symmetry group (in space of orbits).
Keywords
Cite
@article{arxiv.1106.5017,
title = {From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model},
author = {Alexander V. Turbiner},
journal= {arXiv preprint arXiv:1106.5017},
year = {2011}
}
Comments
dedicated to Willard Miller; 20 pages