Abstract
We use a semigroup positivity preserving to prove asymptotic completeness of the wave operators in many cases when they exist.
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References
Kupsch J. and Sandhas W., Commun. Math. Phys. 2, 147–154 (1966).
Kato T. and Kuroda S., in F.E. Browder (ed.), Functional Analysis and Related Fields, Springer Verlag, Berlin, 1970, pp. 99–131.
Kato T., Proceedings of the International Conference on Functional Analysis and Related Topics, Tokyo, April 1969, Tokyo University Press, Tokyo, 1970, pp. 206–215.
Simon B., Quantum Mechanics for Hamiltonians defined as Quadratic Forms, Princeton University Press, Princeton, 1971.
Birman M., Dokl. Akad. Nauk. SSSR 147, 1008–1009 (1962).
Lavine R., Commun. Math. Phys. 20, 301–323 (1971).
Lavine R., J. Funct. Anal. 5, 368–382 (1970).
Robinson, D.W., Ann. I.H.P. 21 (1974).
Semenov, Yu., ‘On the Convergence of Hermitian Forms bounded from below associated with Schrödinger Operators’, to appear in Studia Math.
Kovalenko, V.F. and Semenov, Yu., ‘On Generalized Eigenfunction Expansion for Some Schrödinger Operators with Singular Potentials’, to appear in Uspekhi Mat. Nauk (USSR).
Ladyzhenskaya O.A., Solonnikov V.A., and Ural'tseva N.N., Linear and Quasilinear Equations of Parabolic Type, Nauka, Moskow, 1967.
Kac M., Probability and Related Topics in Physical Sciences, Interscience Publ., New York, 1959.
Pearson D.B., Helv. Phys. Acta 48, 639 (1975).
Deift, P. and Simon, B., ‘On the Decoupling of Finite Singularities from the Question of Asymptotic Completeness in Two-body Quantum Systems’, preprint, Princeton University.
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Semenov, Y.A. Wave operators for the Schrödinger equation with strongly singular short-range potentials. Lett Math Phys 1, 457–461 (1977). https://doi.org/10.1007/BF00399736
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DOI: https://doi.org/10.1007/BF00399736