## Quantum systems related to root systems and radial parts of Laplace operators

*Olshanetsky, M. A.*;

*Perelomov, A. M.*;

- Subject: Mathematical Physics

- References (19) 19 references, page 1 of 2
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[1] Gel'fand, I.M., Center of infinitesimal group ring, Mat. Sb. 26, 103-112 (1950)

[2] Gel'fand, I.M., Spherical functions on symmetric Riemann spaces, Dokl. Akad. Nauk SSSR 70, No.1, 5-8 (1950)

[3] Berezin, F.A., Laplace operators on semisimple Lie groups, Tr. Mosk. Mat. Ob-va 6, 371-463 (1957)

[4] Berezin, F.A. and Karpelevich, F.I., Zonal spherical functions and Laplace operators on certain symmetric spaces, Dokl. Akad. Nauk SSSR 118, No.1, 9-12 (1958)

[5] Olshanetsky, M.A. and Perelomov, A.M., Completely integrable Hamiltonian systems connected with semisimple Lie algebras, Invent. Math. 37, 93-108 (1976)

[6] Bourbaki, N., Lie Groups and Lie Algebras, Addison-Wesley

[7] Calogero, F., Solution of a three-body problem in one dimension, J. Math. Phys. 10, 2191-2196 (1969)

[8] Calogero, F., Solution of the one-dimensional N -body problem, J. Math. Phys. 12, 419-436 (1971)

[9] Perelomov, A.M., Algebraic method of solution of one-dimensional model of N interacting particles, Theor. Math. Phys. 6, 263-283 (1971)

[10] Sutherland, B., Exact results for a quantum many-body problem in one dimension, Phys. Rev. A5, 1372-1376 (1972)

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