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Schrödinger operators with rapidly oscillating central potentials


Author: Denis A. W. White
Journal: Trans. Amer. Math. Soc. 275 (1983), 641-677
MSC: Primary 35P25; Secondary 34B25, 35P10, 81F05
MathSciNet review: 682723
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Abstract: Spectral and scattering theory is discussed for the Schrödinger operators $ H = - \Delta + V$ and $ {H_0} = - \Delta $ when the potential $ V$ is central and may be rapidly oscillating and unbounded. A spectral representation for $ H$ is obtained along with the spectral properties of $ H$. The existence and completeness of the modified wave operators is also demonstrated. Then a condition on $ V$ is derived which is both necessary and sufficient for the Møller wave operators to exist and be complete. This last result disproves a recent conjecture of Mochizuki and Uchiyama.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0682723-7
Article copyright: © Copyright 1983 American Mathematical Society