Open AccessOn the Long-Range Stationary Wave Operator
Author(s) -
Hiroshi Isozaki
Publication year - 1977
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195189601
Subject(s) - mathematics , hilbert space , operator (biology) , scattering theory , d'alembert operator , completeness (order theory) , scattering , schrödinger's cat , quantum graph , range (aeronautics) , mathematical analysis , space (punctuation) , quantum , mathematical physics , quantum mechanics , physics , biochemistry , chemistry , materials science , repressor , transcription factor , composite material , gene , linguistics , philosophy
In the present paper we shall be concerned with the stationary theory of scattering associated with the Schrodinger operator with a long-range potential. In quantum theory of scattering, many authors have investigated the existence and completeness of wave operators W = s-lim ee~y where J-»±oo HI and H2 are self-adjoint operators acting on a Hilbert space M. Among them, Kato and Kuroda gave an abstract time-independent approach to scattering theory. They derived a stationary form of the wave operator in the following way:
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