Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.12202/9197
Title: | Existence and completeness of wave operators in two Hilbert spaces |
Authors: | Schechter, Martin Lebow, Arnold Rosenfeld, Norman Altabet, Meryl J. |
Keywords: | Pure sciences Mathematics Hilbert spaces quantum physics |
Issue Date: | Jun-1984 |
Publisher: | Yeshiva University |
Citation: | Altabet, M. J. (1984, June). Existence and completeness of wave operators in two Hilbert spaces (Publication No. 3331403) [Doctoral dissertation, Yeshiva University]. |
Series/Report no.: | Belfer School of Graduate Dissertations;Publication No. 3331403 |
Abstract: | In this thesis we consider an unperturbed self-adjoint operator H(,0) on a Hilbert space H(,0), the operators A, B mapping H(,0) to the Hilbert space K, and J a bounded linear operator mapping the Hilbert space H(,0) to the Hilbert space H.;Our first objective is to give conditions under which there exists a perturbed self-adjoint operator H such that R(z)J - JR(,0)(z) = -(BJ('*)R(z))*AR(,0)(z) and HJ(R-HOOK)J(H(,0) + B('*)A). We prove the existence of the operator H by actually constructing its resolvent R(z).(').;Our next objective is to consider two specific operators H(,0), the momentum operator and the kinetic energy operator, and to give examples of A, B, J for which the main conclusions of scattering theory hold. In obtaining conditions for the existence and completeness of the wave operator, we use a combination of time dependent and stationary methods. |
Description: | Doctoral dissertation, PhD / Open Access |
URI: | https://ezproxy.yu.edu/login?url=https://www.proquest.com/dissertations-theses/existence-completeness-wave-operators-two-hilbert/docview/303331403/se-2?accountid=15178 https://hdl.handle.net/20.500.12202/9197 |
ISBN: | 9798641266169 |
Appears in Collections: | Belfer Graduate School of Science Dissertations 1962 - 1978 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Altabet - Existence and Completeness of Wave Operators in Two Hilbert Spaces.pdf | 8.93 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License