Essential Aspects of Weakly Nonlinear Relativistic Quantum Electron Optics in a Waveguide
M. A. Grado-Caffaro and M. Grado-Caffaro
Within a new perspective, we present a theoretical formulation to investigate the essential aspects of weakly nonlinear relativistic quantum electron optics in a waveguide. In fact, starting from the nonlinear Dirac equation, we derive important results on the behaviour of relativistic electrons propagating as semilinear solitons in a quasi-one-dimensional electron waveguide. As main result, the electron velocity is determined in the ultrarelativistic case.
Keywords: Nonlinear relativistic quantum electron optics, Nonlinear Dirac equation, Soliton electrons, Electron waveguides, Electron velocity.