Abstract
The eigenvalue problem of the scalar Bethe-Salpeter equation is solved by application of the vertical Dyson representation. The method of solution is developed in complete analogy to the solution of Schrödinger's equation by a Stieltjes representation in the case of a Yukawa potential. The eigenvalues are zeros of a characteristic determinant, which can be understood as a generalization of the nonrelativistic Jost function.
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Kramer, G., Meetz, K. Application of spectral representations to the nonrelativistic and the relativistic Bethe-Salpeter equation. Commun.Math. Phys. 3, 29–52 (1966). https://doi.org/10.1007/BF01645460
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DOI: https://doi.org/10.1007/BF01645460