  We show a new method for analyzing the time evolution of the Schrodinger wave
function Psi(x,t). We propose the decomposition of the Hamiltonian as:
H(t)=Hp(t)+Hc(t), where Hp(t) is the Hamiltonian such that Psi(x,t) is its
instantaneous eigenfunction, and Hc(t) the Hamiltonian which changes the state
Psi. With this decomposition, the action of H(t) on the wave function is
simplified and the Schrodinger equation is in a simpler form which can be
solved more easily. We illustrate this method by exactly solving the
Schrodinger equation for cases of nonspreading wave packets. This method can be
applied as well to analyzing the time evolution of general Hamiltonian systems.
