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

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).

arXiv commentdedicated to Willard Miller; 20 pages

References in corpus (6)

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• Quasi-Exactly-Solvable Many-Body Problems
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Cited by in corpus (4)

• Particular Integrability and (Quasi)-exact-solvability
• Truncated Calogero-Sutherland models
• From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians