From Quantum AN to E₈ Trigonometric Model: Space-of-Orbits View
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
From Quantum AN to E₈ Trigonometric Model: Space-of-Orbits View
|
|
| Creator |
Turbiner, A.V.
|
|
| Description |
A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular integrals. All of them are characterized by (i) a number of polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for exactly-solvable cases, (ii) a factorization property for eigenfunctions, (iii) a rational form of the potential and the polynomial entries of the metric in the Laplace-Beltrami operator in terms of affine-Weyl (exponential) invariants (the same holds for rational models when polynomial invariants are used instead of exponential ones), they admit (iv) an algebraic form of the gauge-rotated Hamiltonian in the exponential invariants (in the space of orbits) and (v) a hidden algebraic structure. A hidden algebraic structure for (A–B–C–D)-models, both rational and trigonometric, is related to the universal enveloping algebra Ugln. For the exceptional (G–F–E)-models, new, infinite-dimensional, finitely-generated algebras of differential operators occur. Special attention is given to the one-dimensional model with BC₁≡(Z2)⊕T symmetry. In particular, the BC₁ origin of the so-called TTW model is revealed. This has led to a new quasi-exactly solvable model on the plane with the hidden algebra sl(2)⊕sl(2).
|
|
| Date |
2019-02-19T18:36:15Z
2019-02-19T18:36:15Z 2013 |
|
| Type |
Article
|
|
| Identifier |
From Quantum AN to E₈ Trigonometric Model: Space-of-Orbits View / A.V. Turbiner // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 24 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 35P99; 47A15; 47A67; 47A75 DOI: http://dx.doi.org/10.3842/SIGMA.2013.003 http://dspace.nbuv.gov.ua/handle/123456789/149207 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|