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Long-range potential scattering by Enss's method in two Hilbert spaces


Author: Denis A. W. White
Journal: Trans. Amer. Math. Soc. 295 (1986), 1-33
MSC: Primary 35P25; Secondary 47A40, 81F05
DOI: https://doi.org/10.1090/S0002-9947-1986-0831186-X
MathSciNet review: 831186
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Abstract: Existence and completeness of wave operators is established by a straightforward transposition of the original short range result of Enss into an appropriate two-Hilbert space setting. Applied to long range quantum mechanical potential scattering, this result in conjunction with recent work of Isozaki and Kitada reduces the problem of proving existence and completeness of wave operators to that of approximating solutions of certain partial differential equations on cones in phase space. As an application existence and completeness of wave operators is established for Schrödinger operators with a long range multiplicative and possibly rapidly oscillating potential.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0831186-X
Article copyright: © Copyright 1986 American Mathematical Society

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