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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147394 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1473942019-02-15T01:23:17Z From Quantum AN (Calogero) to H₄ (Rational) Model Turbiner, A.V. 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). 2011 Article 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. 1815-0659 2010 Mathematics Subject Classification: 35P99; 47A15; 47A67; 47A75 DOI:10.3842/SIGMA.2011.071 http://dspace.nbuv.gov.ua/handle/123456789/147394 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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). |
| format |
Article |
| author |
Turbiner, A.V. |
| spellingShingle |
Turbiner, A.V. From Quantum AN (Calogero) to H₄ (Rational) Model Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Turbiner, A.V. |
| author_sort |
Turbiner, A.V. |
| title |
From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_short |
From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_full |
From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_fullStr |
From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_full_unstemmed |
From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_sort |
from quantum an (calogero) to h₄ (rational) model |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147394 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:27:19Z |
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