  We compute the leading contribution to the effective Hamiltonian of SU(N)
matrix theory in the limit of large separation. We work with a gauge fixed
Hamiltonian and use generalized Born-Oppenheimer approximation, extending the
recent work of Halpern and Schwartz for SU(2). The answer turns out to be a
free Hamiltonian for the coordinates along the flat directions of the
potential. Applications to finding ground state candidates and calculation of
the correction (surface) term to Witten index are discussed.
