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On Scattering for SCHRÖDINGER Operators with Anisotropic and Singular Potentials
Author(s) -
Demuth Michael
Publication year - 1986
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19861290117
Subject(s) - mathematics , pseudodifferential operators , infinity , mathematical proof , scattering , anisotropy , convergence (economics) , schrödinger's cat , feynman diagram , mathematical analysis , mathematical physics , pure mathematics , quantum mechanics , physics , geometry , economics , economic growth
The existence of wave operators is considered for SCHRÖDINGER operators with anisotropic potentials. The potentials may have positive barriers which are allowed to increase up to infinity over unbounded regions in R n . The convergence of the corresponding wave and scattering operators is shown. In the time‐dependent geometric proofs the FEYNMAN‐KAC‐formula is applied essentially.