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

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Literature Cited

  1. 1.

    I. M. Gel'fand, "Center of infinitesimal group ring," Mat. Sb.,26, 103–112 (1950).

  2. 2.

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

  3. 3.

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

  4. 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).

  5. 5.

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

  6. 6.

    N. Bourbaki, Lie Groups and Lie Algebras, Addison-Wesley.

  7. 7.

    F. Calogero, "Solution of a three-body problem in one dimensiona," J. Math. Phys.,10, 2191–2196 (1969).

  8. 8.

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

  9. 9.

    A. M. Perelomov, "Algebraic method of solution of one-dimensional moadel of N interacting particles," Teor. Mat. Fiz.,6, 364–391 (1971).

  10. 10.

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

  11. 11.

    P. J. Gambardella, "Exact results in quantum many-body systems of interacting particles," J. Math. Phys.,16, 1172–1187 (1975).

  12. 12.

    M. Moshinsky and J. Patera, "Canonical transformations and accidental degeneracy," IV, J. Math. Phys.,16, 1866–1875 (1975).

  13. 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. 14.

    J. Wolfes, "On the three-body linear problem with three-body interaction," J. Math. Phys.,15, 1420–1424 (1974).

  15. 15.

    F. Calogero and C. Marchioro, "Exact solution of three-body scattering problem," J. Math. Phys.,15, 1425–1430 (1974).

  16. 16.

    S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York—London (1962).

  17. 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. 18.

    Sh. Araki, "On root systems and an infinitesimal classification of irreducible symmetric spaces," J. Math. Osaka City Univ. (1962).

  19. 19.

    M. A. Olshanetsky and A. M. Perelomov, "Quantum completely integrable systems connected with semisimple Lie algegras," Lett. Math. Phys.,2, 7–13 (1977).

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Additional information

Institute of Theoretical and Experimental Physics. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 12, No. 2, pp. 57–65, April–June, 1978.

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Ol'shanetskii, M.A., Perelomov, A.M. Quantum systems related to root systems, and radial parts of Laplace operators. Funct Anal Its Appl 12, 121–128 (1978). https://doi.org/10.1007/BF01076255

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Keywords

  • Functional Analysis
  • Quantum System
  • Laplace Operator
  • Radial Part