Universal Journal of Physics and Application Vol. 8(3), pp. 193 - 199
DOI: 10.13189/ujpa.2014.020308
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Dynamics of Wave Packets Generated at a Finite Distance from a Scattering Step


F.Carone Fabiani , D.Narducci *, G.F.Cerofolini
CNISM and Department of Materials Science, University of Milano–Bicocca,Via Cozzi 53, 20155 Milano, Italy

ABSTRACT

The scattering process of wave packets is often described recovering the simple monochromatic scheme supposing that the particle comes from −∞ with a sharp momentum distribution, thus allowing for approximations usually used in common calculations of physical quantities involved in the process. In this work, we study the scattering process of a Gaussian wave packet impinging on the step potential, finding out that its dynamics depends on the initial conditions of the incident particle, and in particular on the wave packet origin x0. We propose a semi-classical approximated model to describe the dynamics of the scattering wave packet, also defining a characteristic time interval tf as the time required for the formation of transmitted packet beyond the step. Through a comparison with the numerical solution of the SchrÖdinger equation, our model explains the tf as a function of the origin x0 and spread of the incident wave packet in coordinate space, giving rise to such dependence for a finite distance scattering processes.

KEYWORDS
Scattering, Tunneling Time, Wave Packet Dynamics, Step Potential

Cite this paper
F.Carone Fabiani , D.Narducci , G.F.Cerofolini . "Dynamics of Wave Packets Generated at a Finite Distance from a Scattering Step." Universal Journal of Physics and Application 8.3 (2014) 193 - 199. doi: 10.13189/ujpa.2014.020308.