On superintegrable systems with a position-dependent mass in polar-like coordinates

doi:10.1088/1674-1056/ab9f22

中国物理B ›› 2020, Vol. 29 ›› Issue (10): 100201-.doi: 10.1088/1674-1056/ab9f22

• • 下一篇

Hai Zhang(章海)¹^,†()

收稿日期:2020-03-27 修回日期:2020-06-03 接受日期:2020-06-23 出版日期:2020-10-05 发布日期:2020-10-05
通讯作者: Hai Zhang(章海)

On superintegrable systems with a position-dependent mass in polar-like coordinates

Hai Zhang(章海)†

¹ School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China

Received:2020-03-27 Revised:2020-06-03 Accepted:2020-06-23 Online:2020-10-05 Published:2020-10-05
Contact: ^†Corresponding author. E-mail: haizhang@mail.ustc.edu.cn
About author:
†Corresponding author. E-mail: haizhang@mail.ustc.edu.cn
* Project supported in part by the National Natural Science Foundation of China (Grant No. 11701009), the Natural Science Research Project of Universities in Anhui, China (Grant No. KJ2017A363), and the Natural Science Fund of Anhui Province, China (Grant Nos. 1908085MA01 and 1908085MA22).

摘要/Abstract

Abstract:

For a superintegrable system defined in plane polar-like coordinates introduced by Szumiński et al. and studied by Fordy, we show that the system with a position-dependent mass is separable in three distinct coordinate systems. The corresponding separation equations and additional integrals of motion are derived explicitly. The closure algebra of integrals is deduced. We also make a generalization of this system by employing the classical Jacobi method. Lastly a sufficient condition which ensures flatness of the underlying space is derived via explicit calculation.

Key words: superintegrable system, separation of variables, position-dependent mass, polar-like coordinates, Jacobi method

中图分类号: (Integrable systems)

02.30.Ik

45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.40.Ky (Riemannian geometries)

Hai Zhang(章海). [J]. 中国物理B, 2020, 29(10): 100201-.

Hai Zhang(章海)†. On superintegrable systems with a position-dependent mass in polar-like coordinates[J]. Chin. Phys. B, 2020, 29(10): 100201-.

参考文献 21

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On superintegrable systems with a position-dependent mass in polar-like coordinates

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