## Further analysis of solutions to the time-independent wave packet equations for quantum dynamics: General initial wave packets

In this paper we reexamine, and analyze solutions to, the recently derived time-independent wave packet-Schroedinger (TIWS) and time-independent wave packet-Lippmann--Schwinger (TIWLS) equations. These equations are so named because they are inhomogeneous, with the inhomogeneity being the initial [ital L][sup 2] wave packet from an underlying time-dependent treatment of the dynamics. We explicitly show that a particular solution of the homogeneous Schroedinger equation can be constructed out of two particular solutions of the inhomogeneous TIW equation satisfying causal and anticausal boundary conditions. The structure of this solution of the homogeneous equation is shown to depend sensitively on the nature of themore »