Abstract
Bound state energies, positions and widths of resonances of two-particle systems may be calculated as zeros of an analytic function of the energy, the modified Fredholm determinant of the Lippmann-Schwinger equation. This generates degenerate perturbation theory particularly easily. The method is generalized to the threebody problem. Here too, the bound states and resonances appear as zeros of an analytic function of the energy, the modified Fredholm determinant of a square-integrable kernel. It is proved that the multiplicity of a zero equals the degeneracy of the corresponding eigenvalue.
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Invited talk at the symposium “Theory of lightest nuclei,” Liblice, Czechoslovakia, May 1974.
Work supported in part by the National Science Foundation.
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Newton, R.G. The determinantal method for bound states and resonances of three-particle systems. Czech J Phys 24, 1195–1204 (1974). https://doi.org/10.1007/BF01587205
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DOI: https://doi.org/10.1007/BF01587205