Europhys. Lett.
Volume 67, Number 5, September 2004
Page(s) 695 - 699
Section General
Published online 01 August 2004
Europhys. Lett., 67 (5), pp. 695-699 (2004)
DOI: 10.1209/epl/i2004-10109-6

Solution of the generalized Dirac equation in a time-dependent linear potential: Relativistic geometric amplitude factor

M. Maamache and H. Lakehal

Laboratoire de Physique Quantique et Systemes Dynamiques, Département de Physique Faculté des Sciences, Université Ferhat Abbas de Sétif - Sétif 19000, Algeria

(Received 26 March 2004; accepted in final form 15 June 2004)

We present exact solutions of the Dirac equation for a particle with time-dependent mass moving in a time-dependent linear potential. In addition, we show that the time evolution can be described in terms of classical concept which leads to solve this problem by standard techniques of Hamiltonian mechanics. Geometric amplitude emerges as an adiabatic limit of the exact dynamics.

03.65.Pm - Relativistic wave equations.
03.65.Ge - Solutions of wave equations: bound states.
03.65.Vf - Phases: geometric; dynamic or topological.

© EDP Sciences 2004