Exact solutions of the Schrödinger equation with double ring-shaped oscillator

Chang Yuan Chen; Yuan You; Xiao Hua Wang; Shi Hai Dong

doi:10.1016/j.physleta.2013.04.026

Exact solutions of the Schrödinger equation with double ring-shaped oscillator

Chang Yuan Chen, Yuan You, Xiao Hua Wang, Shi Hai Dong

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

We present the exact solutions of the Schrödinger 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.

Original language	English
Pages (from-to)	1521-1525
Number of pages	5
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	377
Issue number	23-24
DOIs	https://doi.org/10.1016/j.physleta.2013.04.026
State	Published - 16 Sep 2013

Keywords

Double ring-shaped oscillator
Functional analysis method
Super-universal associated Legendre
polynomials

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10.1016/j.physleta.2013.04.026

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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 .",

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T1 - Exact solutions of the Schrödinger equation with double ring-shaped oscillator

AU - Chen, Chang Yuan

AU - You, Yuan

AU - Wang, Xiao Hua

AU - Dong, Shi Hai

N1 - 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 .

PY - 2013/9/16

Y1 - 2013/9/16

N2 - We present the exact solutions of the Schrödinger 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.

AB - We present the exact solutions of the Schrödinger 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.

KW - Double ring-shaped oscillator

KW - Functional analysis method

KW - Super-universal associated Legendre

KW - polynomials

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U2 - 10.1016/j.physleta.2013.04.026

DO - 10.1016/j.physleta.2013.04.026

M3 - Artículo

SN - 0375-9601

VL - 377

SP - 1521

EP - 1525

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 23-24

ER -

Exact solutions of the Schrödinger equation with double ring-shaped oscillator

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Keywords

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