This report is a translation from the Russian of a survey article by L. D. Faddeyev, which appeared in Uspekhi Matem. Nauk., 14, 57 (1959). Our own interest in this article lies in its relevance to the inverse scattering problem—that is, the problem of determining information about a medium from which an electromagnetic wave is reflected, given a knowledge of the reflection coefficient. Similar questions concerning scattering phenomena in other branches of physics, e.g., in quantum mechanics, can be investigated by means of the same theory. We have therefore thought it worth‐while to reproduce and distribute the translation. A good indication of the contents is given in the Introduction.
REFERENCES
1.
2.
C.
Mo/ller
, 22
, No. 19
(1946
).3.
In conformity with established terminology, a state vector will be understood to be an element of Hilbert space in which all operators act.
4.
5.
6.
7.
8.
9.
We shall call the scattering operator in our example the S function.
10.
11.
G. Borg, “Uniqueness theorems in the spectral theory of ” Eleventh Congress of Scan‐danavian Mathematics, held at Trondheim, August 22–25, 1949, pp. 276–287.
12.
13.
14.
15.
I. M.
Gel’fand
and B. M.
Levitan
, Izvest. Akad Nauk S.S.S.R. Ser. matem.
15
, 309
–360
(1951
).16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
The subscript B used throughout and which transliterates into English as V stands, of course, for Volterra.
31.
Absolute constants depending only on C (which may be different) will be denoted by K.
32.
The dot denotes differentiation with respect to s; a bar will denote complex conjugate.
33.
34.
35.
36.
Z. S. Agranovish and V. A. Marchenko, The Inverse Problem in the Quantum Theory of Scattering, Izd. Kharkov Univ., 1960. (An English translation in preparation).
37.
38.
39.
40.
41.
42.
43.
44.
L. A. Chudov, Izd. OIYaI, (1958).
45.
M. G.
Krein
, Integral equations on a half‐line with difference type kernels, Uspekhi Math. Nauk.
13
, 3
(1958
).46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
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© 1963 The American Institute of Physics.
1963
The American Institute of Physics
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