Time-dependent wave-packet forms of Schroedinger and Lippmann-Schwinger equations

Time-independent wave-packet forms of the Schroedinger equation (TIWSE) and Lippmann-Schwinger equation (TIWLSB) have been derived by a partial time-to-energy Fourier transform of L2 wave-packet solutions to the time-dependent Schroedinger equation. The new equations retain the initial wave packet χ(t0) as a ''universal source'' of scattered waves, which applies for all collision energies E contained in the initial wave packet. The relationship between the solution Ψt0(E) of the TIWSE or TIWLSE and the scattering solution Ψ(+)(E) of the standard time-independent Lippmann-Schwinger or Schroedinger equation is given and the method illustrated by a computational application