Summary
In this letter we consider the radial part of the quadratic Laplace-Beltrami operator relative to symmetric spaces with root system of the type An-1 (n = 2, 3 ... ). We calculate the explicit form of its eigenfunctions corresponding to weight diagrams which are regular tetrahedrons in the n-dimensional Euclidean space. We describe also the associated quantum-mechanical problem.
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Prati, M.C. Exact eigenfunctions of some completly integrable systems. Lett. Nuovo Cimento 41, 275–279 (1984). https://doi.org/10.1007/BF02748360
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DOI: https://doi.org/10.1007/BF02748360