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J. Math. Phys. 20, 594 (1979); http://dx.doi.org/10.1063/1.524128 (14 pages)
Spectral and scattering theory for the adiabatic oscillator and related potentials
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Add to FacebookWe consider the Schrödinger operator H=−Δ+V (r) on Rn, where V (r) =a sin(brα)/rβ+VS(r), VS(r) being a short range potential and α≳0, β≳0. Under suitable restrictions on α, β, but always including α=β=1, we show that the absolutely continuous spectrum of H is the essential spectrum of H, which is [0,∞), and the absolutely continuous part of H is unitarily equivalent to −Δ. We use these results to show the existence and completeness of the Møller wave operators. Our results are obtained by establishing the asymptotic behavior of solutions of the equation Hu=zu for complex values of z.
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- Erratum: Spectral and scattering theory for the adiabatic oscillator and related potentials [J. Math. Phys. 20, 594(1979)]
Matania Ben-Artzi et al.
J. Math. Phys. 21, 2471 (1980)JMAPAQ000021000009002471000001
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T. A. Green and O. E. Lanford, J. Math. Phys. 1, 139–45 (1960)JMAPAQ000001000002000139000001.
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