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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147394 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862629893511053312 |
|---|---|
| author | Turbiner, A.V. |
| author_facet | Turbiner, A.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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).
|
| first_indexed | 2025-11-30T10:12:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147394 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T10:12:28Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Turbiner, A.V. 2019-02-14T17:25:44Z 2019-02-14T17:25:44Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147394 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). This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S₄)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From Quantum AN (Calogero) to H₄ (Rational) Model Article published earlier |
| spellingShingle | From Quantum AN (Calogero) to H₄ (Rational) Model Turbiner, A.V. |
| title | 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_short | From Quantum AN (Calogero) to H₄ (Rational) Model |
| title_sort | from quantum an (calogero) to h₄ (rational) model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147394 |
| work_keys_str_mv | AT turbinerav fromquantumancalogerotoh4rationalmodel |