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Paper   IPM / Physic / 7118
School of Physics
  Title:   Relation of the New Calegero Models and XXZ Spin Chains
  Author(s):  V. Karimipour
  Status:   Preprint
  No.:  0
  Year:  1996
  Supported by:  IPM
We extend our previous analysis of the classical integrable models of Calogero in several respects. Firstly we provide the algebraic resaons of their quantum integrability.Secondly we show why these systems allow their initial value problem to be solved in closed form . Furthermore we show that due to their similarity with the above models the classical and quantum Heisenberg magnets with long rang interactions in a magnetic field are also intergrable. Explicit expressions are given for the integrals of motion in involution in the classical case and for the commuting operators in the quantum case.

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