A remark on the unitarity property of the scattering operator

Author:

Kato T.,Kuroda S. T.

Publisher

Springer Science and Business Media LLC

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Reference9 articles.

1. S. T. Kuroda:Nuovo Cimento,12, 431 (1959).

2. Notations such asE 1,L 2(E 1),L 2(0, ∞) etc., will be used in a similar sense. For those notions in the theory of Hilbert space which are used in the following, see (1) and the literature cited in (1).

3. T. Kato:Trans. Amer. Math. Soc.,70, 195 (1951).

4. See (1). ℜ(A) denotes the range of an operatorA.

5. SinceH 12 is an ordinary differential operator, this is a consequence of the theory of eigenfunction expansions. See,e.g., (7), especially §§ 5.2 and 5.3.

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1. Tosio Kato’s work on non-relativistic quantum mechanics, Part 2;Bulletin of Mathematical Sciences;2019-04

2. Tosio Kato’s work on non-relativistic quantum mechanics: part 1;Bulletin of Mathematical Sciences;2018-02-22

3. Aspects of Nonlinear Scattering Theory;Nonlinear Analysis, Function Spaces and Applications Vol. 4;1990

4. Spectral theory of schrödinger operators on euclidean and on non-euclidean spaces;Communications on Pure and Applied Mathematics;1986

5. References;Pure and Applied Mathematics;1981

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