Abstract
We obtain a set of four-dimensional hyperspherical harmonics in closed form. These harmonics are not only quantized with respect to the rotation group (O 2), but are an irreducible basis for the permutation groupS 3. An additional symmetry is found which allows us to write hyperspherical harmonics classified with respect to a 12 element groupS 3×i×O 2. We give a set of three mutually commuting operators whose eigenvalues uniquely characterize each spherical harmonic with respect to degree, symmetry, and angular momentum in the plane.
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Kilpatrick, J.E., Larsen, S.Y. A set of hyperspherical harmonics especially suited for three-body collisions in a plane. Few-Body Systems 3, 75–94 (1987). https://doi.org/10.1007/BF01078739
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DOI: https://doi.org/10.1007/BF01078739