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Quantum systems related to root systems, and radial parts of Laplace operators. (English) Zbl 0407.43012


MSC:

43A85 Harmonic analysis on homogeneous spaces
70H05 Hamilton’s equations

Citations:

Zbl 0388.43010

References:

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[14] J. Wolfes, ”On the three-body linear problem with three-body interaction,” J. Math. Phys.,15, 1420-1424 (1974). · doi:10.1063/1.1666826
[15] F. Calogero and C. Marchioro, ”Exact solution of three-body scattering problem,” J. Math. Phys.,15, 1425-1430 (1974). · doi:10.1063/1.1666827
[16] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York?London (1962). · Zbl 0111.18101
[17] F. A. Berezin, G. P. Pokhil, and V. M. Finkel’berg, ”Schrödinger’s equation for a system of one-dimensional particles with point interaction,” Vestn. Mosk. Gos. Univ., No. 1, 21-28 (1964).
[18] Sh. Araki, ”On root systems and an infinitesimal classification of irreducible symmetric spaces,” J. Math. Osaka City Univ. (1962). · Zbl 0123.03002
[19] M. A. Olshanetsky and A. M. Perelomov, ”Quantum completely integrable systems connected with semisimple Lie algegras,” Lett. Math. Phys.,2, 7-13 (1977). · Zbl 0366.58005 · doi:10.1007/BF00420664
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