Long-range potential scattering by Enss’s method in two Hilbert spaces
- 1 January 1986
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 295 (1) , 1
- https://doi.org/10.1090/s0002-9947-1986-0831186-x
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.Keywords
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