General Derivation of the Time-Independent Wavepacket Schrödinger and Lippmann-Schwinger Equations

Abstract.

We present a new, general derivation and analysis of the time-independent wavepacket Schrödinger and Lippmann-Schwinger equations. These equations retain the memory of the underlying time-dependent quantum description of a system's dynamics for an initial wavepacket that does not originate an infinite distance away from the target. The relationship between the new scattering solutions and those of standard scattering theory is developed in general, and the implications for both computations and the relationship between theory and experiment are given.