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Lax, P. D.; Phillips, R. S.

The acoustic equation with an indefinite energy form and the Schrödinger equation. (English) Zbl 0186.16401

J. Funct. Anal. 1, 37-83 (1967).
Der Inhalt dieser Arbeit entspricht genau einem Teil des Buches der Verff. über “Scattering Theory” (vgl. vorstehendes Referat Zbl 0186.16301).
Reviewer: Joachim Weidmann (Frankfurt/Main)
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Cited in 12 Documents

MSC:

35Lxx Hyperbolic equations and hyperbolic systems
35J10 Schrödinger operator, Schrödinger equation
35P25 Scattering theory for PDEs

Keywords:

acoustic equation; Schrödinger equation; scattering matrix

Citations:

Zbl 0186.16301
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Full Text: DOI

References:

[1] Birman, M. Sh., Conditions for the existence of wave operators, Izv. Akad. Nauk. U.S.S.R., 27, 883-906 (1963) · Zbl 0183.14104
[2] Dolph, C. L.; McLeod, J. B.; Thoe, D., The analytic continuation to the unphysical sheet of the resolvent kernel and the scattering operator associated with the Schrôdinger operator, J. Math. Anal. Appl., 16, 311-332 (1966) · Zbl 0148.35904
[3] Fourès, Y.; Segal, I. E., Causality and analyticity, Trans. Am. Math. Soc., 78, 385-405 (1955) · Zbl 0064.36805
[4] Kato, T., Wave operators and unitary equivalence, Pacific J. Math., 15, 171-180 (1965) · Zbl 0125.34902
[5] Iohvidov, I. S.; Kreǐn, M. G., Am. Math. Soc. Transl., Ser 2, 34, 283-374 (1963) · Zbl 0184.16401
[6] Lax, P. D.; Phillips, R. S., Scattering theory, Bull. Am. Math. Soc., 70, 130-142 (1964) · Zbl 0117.09104
[7] Lax, P. D.; Phillips, R. S., Analytic properties of the Schrödinger scattering matrix, (Perturbation Theory and Its Applications in Quantum Mechanics (1966), Wiley: Wiley New York), 243-254 · Zbl 0193.38302
[8] Lax, P. D.; Phillips, R. S., Scattering Theory (1967), Academic Press: Academic Press New York · Zbl 0214.12002
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