  We give three formulas for meromorphic eigenfunctions (scattering states) of
Sutherland's integrable N-body Schroedinger operators and their
generalizations. The first is an explicit computation of the Etingof-Kirillov
traces of intertwining operators, the second an integral representation of
hypergeometric type, and the third is a formula of Bethe ansatz type. The last
two formulas are degenerations of elliptic formulas obtained previously in
connection with the Knizhnik-Zamolodchikov-Bernard equation. The Bethe ansatz
formulas in the elliptic case are reviewed and discussed in more detail here:
Eigenfunctions are parametrized by a ``Hermite-Bethe'' variety, a
generalization of the spectral variety of the Lame' operator. We also give the
q-deformed version of our first formula. In the scalar sl_N case, this gives
common eigenfunctions of the commuting Macdonald-Rujsenaars difference
operators.
