Instantaneous Bethe-Salpeter Equation and Its Analog： Breit-like Equation

We take the (μ士e干) system as an example, but restrict ourselves to highlight the states with quantum number JP = 0-, to explore the different contents of the instantaneous Bethe-Salpeter (BS) equation and its analog,the relativistic version of Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, since the Breit equation contains extra un-physical solutions,so we point out that it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.

We take the （μ^±e^-＋） system as an example, but restrict ourselves to highlight the states with quantum number J^P = 0^-, to explore the different contents of the instantaneous Bethe-Salpeter （BS） equation and its analog, the relativistic version of Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, since the Breit equation contains extra un-physical solutions, so we point out that it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.