2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150488The 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.20 pages, 1 figure, file in plain LaTeX includes the figureChaotic Dynamicstext