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Quantum phase flow, induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta, preserves the Moyal bracket rather than the Poisson bracket. We derive quantum Hamilton's equations which determine quantum phase flow. The knowledge of quantum phase flow allows to find the evolution of symbols of generic Heisenberg operators. Solutions of quantum Hamilton's equations play the role of quantum characteristics. At any fixed level of accuracy of semiclassical expansion, quantum characteristics can be constructed by solving first-order ordinary differential equations

Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics