Abstract
We study the discrete spectrum of the Bethe-Salpeter equation in the Wick-Cutkosky model and show that for retarding propagators, the variables can be separated, and in the S-wave case, the equation can be reduced to a one-dimensional equation. By using the method of contour integration, we obtain the exact solution of this equation and study the spectrum of relativistic bound states. We discuss the ambiguity of the analytic expression of the wave function that is caused by the presence of a nonphysical variable in the four-dimensional description of relativistic systems.
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