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The existence of wave operators in scattering theory. (English) Zbl 0319.35059

MSC:
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
35E99 Partial differential equations and systems of partial differential equations with constant coefficients
35B20 Perturbations in context of PDEs
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[1] Alsholm, P. K.: Wave operators for long-range scattering. Mimeographed manuscript · Zbl 0359.47006
[2] Alsholm, P. K., Kato, T.: Scattering with long range potentials. In: Partial Differential Equations. Proceedings of Symposia in pure Mathematics. Vol. 23 (Berkeley 1971), pp. 393-399. Providence: American Mathematical Society 1973
[3] Buslaev, V. S., Matveev, V. B.: Wave operators for the Schrödinger equation with a slowly decreasing potential. Theor. math. Phys.2, 266-274 (1970). (English translation from Russian) · doi:10.1007/BF01038047
[4] Cook, J. M.: Convergence to the Møller wave matrix. J. math. Phys.36, 82-87 (1957)
[5] Dollard, J. D.: Asymptotic convergence and the Coulomb interaction. J. math. Phys.5, 729-738 (1964) · doi:10.1063/1.1704171
[6] Dollard, J. D.: Quantum mechanical scattering theory for short-range and Coulomb interactions. Rocky Mountain J. Math.1, 5-88 (1971) · Zbl 0226.35074 · doi:10.1216/RMJ-1971-1-1-5
[7] Haak, M. N.: On convergence to the Møller wave operators. Nuovo Cimento, X Ser.13, 231-236 (1959) · Zbl 0086.42804 · doi:10.1007/BF02727547
[8] Hörmander, L.: Fourier integral operators I, Acta math.127, 79-183 (1971) · Zbl 0212.46601 · doi:10.1007/BF02392052
[9] Jauch, J. M., Zinnes, I. I.: The asymptotic condition for simple scattering systems. Nuovo Cimento, X. Ser.11, 553-567 (1959) · doi:10.1007/BF02726524
[10] Jörgens, K., Weidmann, J.: Zur Existenz der Wellenoperatoren. Math. Z.131, 141-151 (1973) · Zbl 0252.35061 · doi:10.1007/BF01187222
[11] Kuroda, S. T.: On the existence and the unitary property of the scattering operator. Nuovo Cimento, X. Ser.12, 431-454 (1959) · Zbl 0084.44801 · doi:10.1007/BF02745786
[12] Veselic, K., Weidmann, J.: Existenz der Wellenopertoren für eine allgemeine Klasse von Operatoren. Math. Z.134, 255-274 (1973) · Zbl 0264.47012 · doi:10.1007/BF01214098
[13] Veseli?, K., Weidmann, J.: Asymptotic estimates of wave functions and the existence of wave operators. J. Functional Analysis17, 61-77 (1974) · Zbl 0286.47006 · doi:10.1016/0022-1236(74)90004-4
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