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


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


Zbl 0388.43010
Full Text: DOI arXiv


[1] I. M. Gel’fand, ”Center of infinitesimal group ring,” Mat. Sb.,26, 103-112 (1950).
[2] I. M. Gel’fand, ”Spherical functions on symmetric Riemann spaces,” Dokl. Akad. Nauk SSSR,70, No. 1, 5-8 (1950).
[3] F. A. Berezin, ”Laplace operators on semisimple Lie groups,” Tr. Mosk. Mat. Ob-va,6, 371-463 (1957). · Zbl 0091.28201
[4] F. A. Berezin and F. I. Karpelevich, ”Zonal spherical functions and Laplace operators on certain symmetric spaces,” Dokl. Akad. Nauk SSSR,118, No. 1, 9-12 (1958). · Zbl 0078.09203
[5] M. A. Olshanetsky and A. M. Perelomov, ”Completely integrable Hamiltonian systems connected with semisimple Lie algebras,” Invent. Math.,37, 93-108 (1976). · Zbl 0342.58017
[6] N. Bourbaki, Lie Groups and Lie Algebras, Addison-Wesley. · Zbl 1120.17001
[7] F. Calogero, ”Solution of a three-body problem in one dimensiona,” J. Math. Phys.,10, 2191-2196 (1969).
[8] F. Calogero, ”Solution of the one-dimensional N-body problem,” J. Math. Phys.,12, 419-436 (1971).
[9] A. M. Perelomov, ”Algebraic method of solution of one-dimensional moadel of N interacting particles,” Teor. Mat. Fiz.,6, 364-391 (1971).
[10] B. Sutherland, ”Exact results for a quantum many-body problem in one dimension,” Phys. Rev.,A5, 1372-1376 (1972).
[11] P. J. Gambardella, ”Exact results in quantum many-body systems of interacting particles,” J. Math. Phys.,16, 1172-1187 (1975).
[12] M. Moshinsky and J. Patera, ”Canonical transformations and accidental degeneracy,” IV, J. Math. Phys.,16, 1866-1875 (1975).
[13] F. Calogero, C. Marchioro, and O. Ragnisco, ”Exact solution of the classical and quantal one-dimensional many-body problem,” Lett. N. C.,13, 383-388 (1975).
[14] J. Wolfes, ”On the three-body linear problem with three-body interaction,” J. Math. Phys.,15, 1420-1424 (1974).
[15] F. Calogero and C. Marchioro, ”Exact solution of three-body scattering problem,” J. Math. Phys.,15, 1425-1430 (1974).
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.