Classical and Quantum Superintegrability of Stackel Systems

被引：4

作者：

Blaszak, Maciej ^{[1
]}

Marciniak, Krzysztof ^{[2
]}

机构：

[1] Adam Mickiewicz Univ, Div Math Phys, Fac Phys, Poznan, Poland

[2] Linkoping Univ, Dept Sci & Technol, Campus Norrkoping, Linkoping, Sweden

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2017年 / 13卷

关键词：

Hamiltonian systems; classical and quantum superintegrable systems; Stackel systems; Hamilton-Jacobi theory; Stackel transform; INTEGRABLE HAMILTONIAN-SYSTEMS; DIMENSIONAL CURVED SPACES; MAXIMAL SUPERINTEGRABILITY; BENENTI SYSTEMS;

D O I：

10.3842/SIGMA.2017.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stackel transform to preserve maximal superintegrability and we apply this condition to our class of Stackel systems, which yields new maximally superintegrable systems as conformal deformations of the original systems. Further, we demonstrate how to perform the procedure of minimal quantization to considered systems in order to produce quantum superintegrable and quantum separable systems.

引用

页数：23

共 24 条

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