  Quantization of energy balance equations, which describe a separatrix -- like
motion is presented. The method is based on an exact canonical transformation
of the energy--time pair to the action-angle canonical pair, $ (E,t)\to
(I,\theta) $. Quantum mechanical dynamics can be studied in the framework of
the new Hamiltonian. This transformation also establishes a relation between a
wide class of the energy balance equations and dynamical localization of
classical diffusion by quantum interference, that was studied in the field of
quantum chaos. An exact solution for a simple system is presented as well.
