Time-independent wave packet theory of collisions

V. S. Olkhovsky, Erasmo Recami

C. L. Hammer, Vaughn Stephen Zidell, T. Weber

Wei Kang Zhu, Youhong Huang, Donald Jack Kouri +2 more

Time-independent wave-packet forms of the Schr\"odinger equation (TIWSE) and Lippmann-Schwinger equation (TIWLSB) have been derived by a partial time-to-energy Fourier transform of ${\mathit{L}}^{2}$ wave-packet solutions to the time-dependent Schr\"odinger equation. The new equations retain the initial wave packet \ensuremath{\chi}(${\mathit{t}}_{0}$) 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 ${\mathrm{\ensuremath{\Psi}}}_{\mathit{t}0}$(E) of the TIWSE or TIWLSE and the scattering solution ${\mathrm{\ensuremath{\Psi}}}^{(+)}$(E) of the standard time-independent Lippmann-Schwinger or Schr\"odinger equation is given and the method illustrated by a computational application.

Sergej A. Lebedeff

In the present investigation the semiclassical approximation using the time-dependent formulation of the collision theory is extended. The previously used narrow-wave-packet approximation is improved by using, instead of expanding wave packets, wave packets that first contract and then expand. In addition, an integral equation is derived that allows one to obtain corrections to the narrow-wave-packet approximation. Several of these corrections are presented.

Ángel S. Sanz, Salvador Miret-Artés

V. D. Kamenetskii