On the solutions of the Wick-Cutkosky model in the instantaneous approximation
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By reexamining the analysis of Basu and Biswas, based on the stereographic projection method of Fock and Levy, it is shown that the general solution of the Wick-Cutkosky model in the instantaneous approximation, hitherto unreported, involves only one quantum number; this is contrasted with the well-known solution which involves two quantum numbers, but for which the spectrum is degenerate with respect to one of them. The latter situation is shown to hold under a rather special circumstance.
KeywordsBethe-Salpeter equation Wick-Cutkosky model stereographic projection Funk-Hecke theorem second order difference equation infinite continued fraction
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