Wavepacket propagation Solving the time-dependent Schrodinger equation

Wavepacket propagation Solving the time-dependent Schrodinger equation 

If the hamiltonian H is not dependent on the time t, the solution of the above equation becomes 

The equation enables us to relate the wavefunction at time t t to that at time t. It is only valid if the hamiltonian is not an explicit function of time. The most straightforward way to see what is implied by this equation is to expand the exponential on the right hand side of eq. (1.2). 

This expansion shows clearly what is needed to solve the TDSE. We must be able to operate with the hamiltonian operator on the wavefunction to generate a new function. 

Jakubetz (ed.), Methods in Reaction Dynamics Springer-Verlag Berlin Heidelberg 2001 

---