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We show a new method for analyzing the time evolution of the Schrodinger wavefunction 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 itsinstantaneous eigenfunction, and Hc(t) the Hamiltonian which changes the statePsi. With this decomposition, the action of H(t) on the wave function issimplified and the Schrodinger equation is in a simpler form which can besolved more easily. We illustrate this method by exactly solving theSchrodinger equation for cases of nonspreading wave packets. This method can beapplied as well to analyzing the time evolution of general Hamiltonian systems.

Analyzing the Time Evolution of Wave Functions by Decomposing the Hamiltonian into State-Preserving and State-Changing Hamiltonians