Dinâmica quântica de uma partícula neutra em campos elétricos externos.

Abstract

This work aims to study the planar quantum dynamics of neutral particles of spin-1/2 in the presence of electric fields. A priori a particle with null charge should not interact with electromagnetic fields, but to admit particles having magnetic dipole moment, we see that the interaction is possible. Such study happen through the Dirac equation with non-minimal coupling, where the interaction term takes into account the magnetic dipole moment, spin of the particle and electromagnetic field. From this equation, we derive and solve two differential equations of first order, showing that the solutions is linked to spin. The solutions to the Aharonov-Casher effect is discussed in detail for the first time in this study. We also derive a differential equation of second order, from which we obtained the energy levels for a particle moving in a constant radius circular path. In addition, using the self-adjoint extension method, we find wave functions of bound states and energy levels to the full space, including the region r = 0. The Energy levels obtained are analogous to Landau levels, and show a dependence on the spin projection parameter. Finally, we take the non-relativistic limit for the full space.