Abstract
The Schrodinger operator H=−Δ+V is considered when the potential V is central, oscillating and possibly unbounded. An eigenfunction expansion for H is derived. Also, the phase shift of the generalized eigenfunctions of H is computed. The expansion and shift are, together, applied to the study of the wave operators of scattering theory. The modified wave operators, for H and H0=−Δ are shown to exist and be complete and a condition on V is derived which is necessary and sufficient for the Moller wave operators to exist and be complete. Spectral properties of H are also discussed.
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