Quantum Super-Integrable Systems as Exactly Solvable Models

被引：24
|
作者：
Fordy, Allan P. [1 ]
机构：
[1] Univ Leeds, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷
关键词：
quantum integrability; super-integrability; exact solvability; Laplace-Beltrami;
D O I：
10.3842/SIGMA.2007.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页数：10
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