From Quantum A N (Calogero) to H 4 (Rational) Model

[摘要] 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).

[关键词] (quasi)-exact-solvability;rational models;algebraic forms;Coxeter (Weyl) invariants;hidden algebra