Invariants, Green's function, and coherent states of dynamical systems

The relation between the Green function of a dynamical system and the integrals of the motion which are the operators of initial coordinates and momenta of the system is obtained. The Green function of a system with rather arbitrary hamiltonian, both hermitian and nonhermitian, is shown to be the eigenfunction of the invariant operator of initial coordinate. The quantum system with general quadratic hamiltonian and the singular nonstationary oscillator are discussed as examples.