Abstract
The explicit form of the Laplace-Beltrami operator Δ LB on symmetric space X SO 0(2,3)/ SO(2) x SO(3) of rank 2 is given. Using the representation of SO 0(2,3) the eigenfunctions of δ LB, i.e. plane waves on X are constructed. The integral representation of the zonal spherical functions of the group SO o(2, 3) is presented and the related 2-body one-dimensional quantum systems are considered.
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