TY - JOUR
T1 - Spectral and scattering theory for the adiabatic oscillator and related potentials
AU - Ben-Artzi, Matania
AU - Devinatz, Allen
PY - 1978
Y1 - 1978
N2 - We consider the Schrödinger operator H = -Δ+V(r) on R n, where V(r) = a sin(br α)/r β+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.
AB - We consider the Schrödinger operator H = -Δ+V(r) on R n, where V(r) = a sin(br α)/r β+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.
UR - http://www.scopus.com/inward/record.url?scp=36749111712&partnerID=8YFLogxK
U2 - 10.1063/1.524128
DO - 10.1063/1.524128
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AN - SCOPUS:36749111712
SN - 0022-2488
VL - 20
SP - 594
EP - 607
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 4
ER -