Breit Equation versus Salpeter Equation in One Dimension

We compare bound-state solutions of the Breit equation and the Salpeter equation for a relativistic two-body system in one dimension. In particular, we examine how the solutions behave as the interaction range is varied. While the solutions of the two equations are similar when the interaction range is not very small, they become very different in the short-range limit. This clarifies intriguing aspects of the results recently found by Munakata et al.