  We study the microlocal structure of the resolvent of the semi-classical
Schrodinger operator with short range potential at an energy which is a unique
non-degenerate global maximum of the potential. We prove that it is a
semi-classical Fourier integral operator quantizing the incoming and outgoing
Lagrangian submanifolds associated to the fixed hyperbolic point. We then
discuss two applications of this result to describing the structure of the
spectral function and the scattering matrix of the Schrodinger operator at the
critical energy.
