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Teoreticheskaya i Matematicheskaya Fizika, 1972, Volume 10, Number 2, Pages 238–248
(Mi tmf2661)
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This article is cited in 15 scientific papers (total in 15 papers)
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.
Received: 15.12.1970
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
Linking options:
https://www.mathnet.ru/eng/tmf2661 https://www.mathnet.ru/eng/tmf/v10/i2/p238
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