from quantum an to e8 trigonometric model: space-of-orbits view
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2013
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Abstract
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≡(Z_2)⊕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).
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turbiner2013symmetry,from
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| Authors | ;Alexander V. Turbiner |
| Journal | Therapeutic drug monitoring |
| Year | 2013 |
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| Keywords | Keywords not found |
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