Wave packet formulation

D. Baye, M. Dufour, Benjamin Fuks E

Sergej A. Lebedeff

A semiclassical approximation is presented which uses the wave-pocket formulation of collision theory. First an appropriate semiclassical approximation is derived by assuming that the wave packet is and remains narrow during the passage of the interaction region. After this, a process is devised to decompose a macroscopic wave packet into narrow wave packets. The wave function, after the collision, is obtained by summing up the contributions from all the narrow wave packets into which the macroscopic wave packet was decomposed. Finally, using this function, the $S$ matrix and the scattering cross section are calculated.

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.

V. S. Olkhovsky, V. Petrillo, Aleksandr K. Zaichenko

The explicit formulation of the initial conditions of the definition of the wave-packet tunneling time is proposed. This formulation takes adequately into account the irreversibility of the wave-packet space-time spreading. Moreover, it explains the violations of the Hartman effect, leading to a strong decrease of the tunneling times up to negative values for wave packets with large momentum spreads due to strong wave-packet time spreading.