Eigenvalues of Ruijsenaars-Schneider models associated with A(n-1) root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with A(n-1) root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are given in terms of the Bethe ansatz formulas. Taking the "nonrelativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder (C) 2004 American Institute of Physics