We propose a class of analytic short‐ranged nonlocal potentials, and we obtain dispersion relations for the forward scattering amplitude. We use the Fredholm method for the Lippman‐Schwinger equation for the scattering solution, and contour rotation in the analytic continuation of the forward scattering amplitude.
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We have not proved that a negative energy bound state or bound states give rise to a pole in the forward scattering amplitude.
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W. V. Lovitt, Linear Integral Equations (Dover, New York, 1950). The discussions in this reference are concerned with continuous functions on a bounded interval. However, the arguments and the results remain valid in all cases discussed below where Ref. 35 is quoted.
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The result, proved in Ref. 38 for functions of one complex variable, may be extended to the case of functions of two complex variables.
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D. V. Widder, The Laplace Transform (Princeton U.P., Princeton, N.J., 1946), Corollary la, p. 182.
41.
We shall obtain in Appendix B a result on functions of two complex variables which enables us to give a set of sufficient conditions for to satisfy condition (C).
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See Appendix C.
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See Ref. 39.
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© 1973 The American Institute of Physics.
1973
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