Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 1, January 2005, Pages 660 - 675

Quasi-Exactly Solvable Hamiltonians related to Root Spaces

Authors
Alexander V. Turbiner
Corresponding Author
Alexander V. Turbiner
Available Online 1 January 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.51How to use a DOI?
Abstract
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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - Supplement 1
Pages
660 - 675
Publication Date
2005/01
ISBN
91-974824-3-9
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.51How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Alexander V. Turbiner
PY  - 2005
DA  - 2005/01
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  - https://doi.org/10.2991/jnmp.2005.12.s1.51
ID  - Turbiner2005
ER  -