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 TMF, 1972, Volume 10, Number 2, Pages 238–248 (Mi tmf2661)

Scattering problem for radial Schrödinger equation with a slowly decreasing potential

V. B. Matveev, M. M. Skriganov

Abstract: The scattering problem for the Schrodinger equation with slowly decreasing potential is considered. Stationary wave operators $W_{\pm}(H,H_0)$ are constructed and their completeness is proved. It is shown that the operators $W_{\pm}(H,H_0)$ can also be defined as the limits $W_{\pm}(H,H_0)=\lim{t\to\pm\infty} \exp(itH)T_{\pm}\exp(-itH_0)$, $T_{\pm}$ being some operators, which do not depend on $t$, do not commute with $H_0$ and can be constructed explicity for the :given potential $q(x)$.The invariance principle for the wave operators $W_{\pm}$ is proved.

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English version:
Theoretical and Mathematical Physics, 1972, 10:2, 156–164

Bibliographic databases:

Citation: V. B. Matveev, M. M. Skriganov, “Scattering problem for radial Schrödinger equation with a slowly decreasing potential”, TMF, 10:2 (1972), 238–248; Theoret. and Math. Phys., 10:2 (1972), 156–164

Citation in format AMSBIB
\Bibitem{MatSkr72} \by V.~B.~Matveev, M.~M.~Skriganov \paper Scattering problem for radial Schr\" odinger equation with a slowly decreasing potential \jour TMF \yr 1972 \vol 10 \issue 2 \pages 238--248 \mathnet{http://mi.mathnet.ru/tmf2661} \zmath{https://zbmath.org/?q=an:0254.47018} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 10 \issue 2 \pages 156--164 \crossref{https://doi.org/10.1007/BF01090727}