From Quantum AN (Calogero) to H₄ (Rational) Model
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 fac...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147394 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | From Quantum AN (Calogero) to H₄ (Rational) Model / A.V. Turbiner // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |