Explorations of many-body relativistic wave equations within a one-dimensional model

Abstract

A one-dimensional analog that reflects many of the features of the many-body Dirac equation is considered. The model can be solved numerically using a convenient finite basis discrete variable representation. Both an (unbound) harmonic oscillator potential and a (bound) inverse Gaussian one-particle potential are discussed for interacting particles. In a second thread in the paper, the mass term is neglected in the model many-body Dirac equation, and it is shown that the original equation, which has 2N coupled components for N particles can then be reduced to 2N decoupled one-component equations, which can be solved “analytically” for arbitrary many particles interacting through central two-body potentials.