Quasi-Exactly Solvable Hamiltonians related to Root Spaces

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  -