From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model

Details From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model

2011-06-24

arxiv.org/abs/1106.5017v2

SIGMA 7 (2011), 071

Physics

Mathematical Physics

dedicated to Willard Miller; 20 pages

Scientific paper

10.3842/SIGMA.2011.071

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).

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