Calogero Model with Different Masses

Ancilla Nininahazwe

Université du Burundi, Institut de Pédagogie Appliquée, Bujumbura, Burundi.

DOI: 10.4236/ojm.2013.33011                

Abstract

We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Here, we factorize the ground stateout of the Hamiltonian H in order to get the new operatorwhich preserves some spaces of polynomialsin 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.

Keywords

Multispecies One-Dimensional Calogero; Equal Masses; Different Masses; Usual Calogero Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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
[2]	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
[3]	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
[4]	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
[5]	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
[6]	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
[7]	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
[8]	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