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Calogero Model with Different Masses
Université du Burundi, Institut de Pédagogie Appliquée, Bujumbura, Burundi
- 1 Université du Burundi, Institut de Pédagogie Appliquée, Bujumbura, Burundi
Open Journal of Microphysics·Volume 03 (2013)·Pages 60–63·Published 9 August 2013·DOI10.4236/ojm.2013.33011
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Abstract
We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Here, we factorize the ground state out of the Hamiltonian H in order to get the new operator which preserves some spaces of polynomials in the case of equal masses, i . e . (the usual Calogero model) and in the case with different masses. The spectrum of these both cases is found easily.
KeywordsMultispecies One-Dimensional CalogeroEqual MassesDifferent MassesUsual Calogero Model
- F. Calogero, “Solution of a Three-Body Problem in One Dimension,” Journal of Mathematical Physics, Vol. 10, No. 12, 1969, pp. 2191-2197. doi:10.1063/1.1664820
- F. Calogero, “Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials,” Journal of Mathematical Physics, Vol. 12, No. 3, 1971, p. 419. doi:10.1063/1.1665604
- M. A. Olshanetsky and A. M. Perelomov, “Classical Integrable Finite-Dimensional Systems Related to Lie Algebras,” Physics Reports, Vol. 71, No. 5, 1981, pp. 313-400. doi:10.1016/0370-1573(81)90023-5
- V. Bardek, L. Jonke, S. Meljanac and M. Milchovic, “Calogero Model, Deformed Oscillators and the Collapse,” Physical Letters, Vol. B531, No. 3-4, 2002, pp. 311-315. doi:10.1016/S0370-2693(02)01481-8
- S. Meljanac, M. Milekovic and A. Samsarov, “A Multispecies Calogero Model,” Physical Letters, Vol. B573, 2003, pp. 202-208. doi:10.1016/j.physletb.2003.08.029
- W. Ruhl and A. Turbiner, “Exact Solvability of the Calogero and Sutherland Models,” Modern Physics Letters A, Vol. 10, No. 29, 1995, p. 2213. doi:10.1142/S0217732395002374
- A. Turbiner, “Quasi-Exactly-Solvable Problems and sl(2) Algebra,” Communications in Mathematical Physics, Vol. 118, No. 3, 1988, pp. 467-474. doi:10.1007/BF01466727
- Y. Brihaye and A. Nininahazwe, “On Pt-Symmetric Extensions of the Calogero and Sutherland Models,” International Journal of Modern Physics A, Vol. 19, No. 26, 2004, pp. 4391-4400. doi:10.1142/S0217751X04019858