Semi-classical approximation in quantum mechanics

The multi-dimensional semi-classical approximation to equations of quantum mechanics is discussed. The first part is devoted to quantization of the velocity field for general Hamiltonians. The second part is concerned with the semi-classical approximation of the Cauchy problem for the initial data satisfying the correspondence principle, with the scattering problem, and with the asymptotics of spectral series for relativistic, as well as non-relativistic, equations of quantum mechanics. (Auth.)