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.

引用

页数：10

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