Quasi-Exactly Solvable Hamiltonians related to Root Spaces
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sl(2)-Quasi-Exactly-Solvable (QES) generalization of the rational An, BCn, G2, F4, E6,7,8 Olshanetsky-Perelomov Hamiltonians including many-body Calogero Hamiltonian is found. This generalization has a form of anharmonic perturbations and it appears naurally when the original rational Hamiltonian is written in a certain Weyl-invariant polynomial variables. It is demonstrated that for the QES Hamiltonian there eists a finite-dimensional invariant subspace in inhomogeneous polynomials. Eigefunctions and corresponding eigenvalues which belong to this subspace are calculated algebraically.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
TY - JOUR AU - Alexander V. Turbiner PY - 2005 DA - 2005/01/01 TI - Quasi-Exactly Solvable Hamiltonians related to Root Spaces JO - Journal of Nonlinear Mathematical Physics SP - 660 EP - 675 VL - 12 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.s1.51 DO - 10.2991/jnmp.2005.12.s1.51 ID - Turbiner2005 ER -