  A nonperturbative procedure of solving the time-dependent Schr\"odinger
equation, called the multi-projection approach or phase dynamics of quantum
mechanics, is derived and illustrated. In addition to introducing a method with
that time-dependent systems become solvable (under the assumption that
corresponding time-independent systems are solvable), the new approach unveils
several misconcepts related to the usual wavefunction expansion and the
standard perturbation theory.
