Quantum Super-Integrable Systems as Exactly Solvable Models
数学物理
2008-04-24 v1 math.MP
可精确求解与可积系统
摘要
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are constructed through the action of the commuting operators. Finite dimensional representations of the quadratic algebras are thus constructed in a way analogous to that of the highest weight representations of Lie algebras.
引用
@article{arxiv.math-ph/0702048,
title = {Quantum Super-Integrable Systems as Exactly Solvable Models},
author = {Allan P. Fordy},
journal= {arXiv preprint arXiv:math-ph/0702048},
year = {2008}
}
备注
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/