Quantum evolution of the localized state

An over-complete set of coherent states in the trajectory parametrization is built for a many-dimensional system with a Hamiltonian quadratic in momenta and coordinates. This parametrization enables us to solve consistently the problem of the vacuum state in the coherent state system. The connection between localized states and classical trajectories is shown. We obtain the approximate expression for the Wigner function of the localized state for a system with a nonquadratic nonstationary Hamiltonian.