TIME-INDEPENDENT WAVE-PACKET FORMS OF SCHRODINGER AND LIPPMANN-SCHWINGER EQUATIONS

Time-independent wave-packet forms of the Schrodinger equation (TIWSE) and Lippmann-Schwinger Schwinger equation (TIWLSE) have been derived by a partial time-to-energy Fourier transform of L2 wave-packet solutions to the time-dependent Schrodinger equation. The new equations retain the initial wave packet chi(tau0) 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 psi(tau)0(E) of the TIWSE or TIWLSE and the scattering solution psi(+)(E) of the standard time-independent Lippmann-Schwinger or Schrodinger equation is given and the method illustrated by a computational application.