Coulomb Scattering. I. Single Channel
1.J. M. Jauch, Helv. Phys. Acta 31, 127 (1958).
2.J. M. Jauch, Helv. Phys. Acta 31, 661 (1958).
3.C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics (Springer‐Verlag, Berlin, 1967), see Chap. V.
4.C. Moller, Kgl. Danske. Videnskab. Selskab. Math.‐Fys. Medd. 23, No. 1 (1945).
5.J. M. Cook, J. Math. Phys. 36, 82 (1957).
6.We are here assuming that is the conventional free Hamiltonian More generally, one must restrict oneself to that part of which is the absolutely continuous (or continuum) part of (see Ref. 7).
7.S. T. Kuroda, Nuovo Cimento 12, 431 (1959).
8.M. N. Hack, Nuovo Cimento 9, 731 (1958).
9.J. M. Jauch and I. I. Zinnes, Nuovo Cimento 11, 553 (1959).
10.I. I. Zinnes, Nuovo Cimento Suppl. 12, 87 (1959).
11.J. D. Dollard, thesis, Princeton University, 1963.
12.We are here emphasizing the limit A similar discussion can be carried out for the limit In addition, we use the notation Φ without explicit time dependence to represent a Schrödinger state at i.e.,
13.T. Ikebe, Archiv Ratl. Mech. Anal. 5, 1 (1960).
14.L. I. Schiff, Quantum Mechanics (McGraw‐Hill Book Co., New York, 1955), p. 116.
15.J. D. Dollard, J. Math. Phys. 5, 729 (1964).
16.L. Schwartz, Théorie des distributions (Herman Cie., Paris, 1959), Vol. II.
17.Here and in the sequel, whenever multiple integrals are replaced by iterated integrals so that integration by parts can be carried out, the replacement can be justified by an application of Fubini’s theorem.
18.Here, as well as in similar situations below, tedious details are omitted. The interested reader may refer to the thesis of one of the authors (D. M.) for these details.
19.L. J. Slater, Confluent Hypergeometric Functions (Cambridge University Press, Cambridge, 1960). See especially formula (4.1.6).
20.N. N. Lebedev, Special Functions and their Applications (Prentice‐Hall, Englewood Cliffs, N.J., 1965). On page 269, there is a useful form for the remainder which permits one to estimate the contribution of k which appears in more than the principal argument of the Kummer function [see Eq. (11)].
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