Phase shifts and the modified and møller wave operators |
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| Authors: | D A W White |
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| Institution: | (1) Stanford University, 94305 Stanford, California, USA;(2) Present address: Department of Mathematics, California Institute of Technology, 91125 Pasadena, California, USA |
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| Abstract: | The Schrödinger 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 H 0=?Δ are shown to exist and be complete and a condition on V is derived which is necessary and sufficient for the Møller wave operators to exist and be complete. Spectral properties of H are also discussed. |
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