Abstract
Abstract We present the exact solutions of the Schrodinger equation with the double ring-shaped oscillator (DRSO) potential. By introducing a new variable x = cos θ 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.
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