No abstract

The Dirac equation, with minimal coupling, is analysed in order to show that the Zitterbewegung (rapid oscillatory motion) also arises when a static and uniform magnetic field is taken into account. The corresponding equations of motion are solved in the Heisenberg picture with the weak-field approximation.

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most students of undergraduate courses, basic or intermediate.

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail.Comment: 14 pages, 4 figures, misprints and figures correcte