Schrödinger operators with rapidly oscillating central potentials
Denis A. W. White
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Source: Crossref
Published: Jan 1, 1983
DOI: 10.1090/s0002-9947-1983-0682723-7
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Spectral and scattering theory is discussed for the Schrödinger operators H = − Δ + V H = - \Delta + V and H 0 = − Δ {H_0} = - \Delta when the potential V V is central and may be rapidly oscillating and unbounded. A spectral representation for H H is obtained along with the spectral properties of H H . The existence and completeness of the modified wave operators is also demonstrated. Then a condition on V 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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