@article{fb2c62614aa44eec8471c6562ad6daee,
title = "Exact solutions of the Schr{\"o}dinger equation with double ring-shaped oscillator",
abstract = "We present the exact solutions of the Schr{\"o}dinger equation with the double ring-shaped oscillator (DRSO) potential. By introducing a new variable x=cosθ and constructing super-universal associated Legendre polynomials we express the polar angular wave functions explicitly. We observe that the present DRSO has caused the symmetry breaking from the original spherical oscillator SU(3)∪SO(3) ∪O(2) symmetries to the present O(2) symmetry due to the surrounded two ring-shaped inversed square potentials. Some special cases are also discussed.",
keywords = "Double ring-shaped oscillator, Functional analysis method, Super-universal associated Legendre, polynomials",
author = "Chen, {Chang Yuan} and Yuan You and Wang, {Xiao Hua} and Dong, {Shi Hai}",
note = "Funding Information: We thank the referees for making invaluable criticisms and positive suggestions which have improved the manuscript. This work is supported by the National Natural Science Foundation of China under Grant No. 11275165 and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291 and partly by 20131150-SIP-IPN , Mexico .",
year = "2013",
month = sep,
day = "16",
doi = "10.1016/j.physleta.2013.04.026",
language = "Ingl{\'e}s",
volume = "377",
pages = "1521--1525",
journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",
issn = "0375-9601",
number = "23-24",
}