Inverse scattering. IV. Three dimensions: generalized Marchenko construction with bound states, and generalized Gel’fand–Levitan equations

Author:

Newton Roger G.1

Affiliation:

1. Physics Department, Indiana University, Bloomington, Indiana 47405

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference16 articles.

1. R. G. Newton, J. Math. Phys. 21, 1698 (1980) JMAPAQ0022-2488

2. and R. G. Newton, 22, 631 (1981); these papers will be referred to as II.JMAPAQ0022-2488, J. Math. Phys.

3. R. G. Newton, J. Math. Phys. 22, 2191 (1981); this paper will be referred to as III.JMAPAQ0022-2488

4. See Sec. 5 of III. Some of the contents of Sec. 6 and all of Secs. 7 and 8 were already contained in the preprint of III, but they were omitted from the published version as the generalized GL equation then lacked foundation.

5. A reminder of our notation:† stands for the adjoint, ⋅for the operator whose kernel is the complex conjugate,∼ for the operator whose kernel is the transpose; Q is the operator with the property (Q,f) (θ) = f(−θ) for f∈L2(S2); and SL2(R) is the class of functions R→B that are square integrable in the strong sense, as defined in the Corollary to Lemma 3.2 of II. Îdenotes the function in L2(S2),l̂(θ) ≡ 1;x̂ denotes the unit vector in R3 x̂ = x/|x|.

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