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
DOI:
https://doi.org/10.1090/S0002-9947-1983-0682723-7
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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© Copyright 1983
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