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This article is cited in 5 scientific papers (total in 5 papers)
From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model
Alexander V. Turbiner Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., Mexico
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:
(quasi)-exact-solvability; rational models; algebraic forms; Coxeter (Weyl) invariants, hidden algebra.
Received: February 28, 2011; in final form July 12, 2011; Published online July 18, 2011
Citation:
Alexander V. Turbiner, “From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model”, SIGMA, 7 (2011), 071, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma629 https://www.mathnet.ru/eng/sigma/v7/p71
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Abstract page: | 161 | Full-text PDF : | 42 | References: | 43 |
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