General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

Abstract

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.