We develop a general `classicalization' procedure that links Hilbert-space and phase-space operators, using Weyl's operator. Then we transform the time-dependent Schrödinger equation into a phase-space picture using free parameters. They include position Q and momentum P. We expand the phase-space Hamiltonian in an ℏ-Taylor series and fix parameters with the condition that coefficients of ℏ0, -iℏ1 ∂/∂Q and iℏ1 ∂/∂P vanish. This condition results in generalized Hamilton equations and a natural link between classical and quantum dynamics, while the quantum motion-equation remains exact. In this picture, the Schrödinger equation reduces in the classical limit to a generalized Liouville equation for the quantum-mechanical system state. We modify Glauber's coherent states with a suitable phase factor S(Q,P,t) and use them to obtain phase-space representations of quantum dynamics and quantum-mechanical quantities.