  The paper presents exact surface of section reduction of quantum mechanics.
The main theoretical result is a decomposition of the energy-dependent
propagator G(E) = (E - H)^(-1) in terms of the propagators which (also or
exclusively) act in Hilbert space of complex-valued functions over the
configurational surface of section, which has one dimension less than the
original configuration space. These energy-dependent quantum propagators from
and/or onto the configurational surface of section can be explicitly
constructed as the solutions of the first order nonlinear Riccati-like initial
value problems.
