Physics – Mathematical Physics
Scientific paper
2003-09-10
Czech.J.Phys. 53 (2003) 1061-1067
Physics
Mathematical Physics
7 pages, LaTeX, submitted to Proceedings of the 12th International Colloquium Quantum Group and Integrable Systems, Prague, 12
Scientific paper
10.1023/B:CJOP.0000010534.58542.
It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions are obtained by pure algebraic means. For both systems new variables are introduced in which the Hamiltonian has an algebraic form being also (block)-triangular. These variables are a certain invariants of the $F_4$ Weyl group. Both Hamiltonians preserve the same (minimal) flag of spaces of polynomials, which is found explicitly.
López Vieyra Juan C.
Turbiner Alexander
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