|
Teoreticheskaya i Matematicheskaya Fizika, 1971, Volume 8, Number 1, Pages 49–54
(Mi tmf4357)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Invariance principle for generalized wave operators
V. B. Matveev
Abstract:
In a Hilbert space $\mathfrak H$ a study is made of limits of the form $W_{\pm}(H,H_0|\Lambda)=\displaystyle\operatornamewithlimits{s-lim}_{t\to\pm\infty}\exp\{it H\}\Lambda(t)$
it being assumed that $\varphi(H)W_{\pm}=W_{\pm}\varphi(H_0)$ for any function $\varphi$ that the operators $H$ and $H_0$ are selfadjoint, and that $\Lambda(t)$ is bounded. The invariance principle states that the limit
$\displaystyle\operatornamewithlimits{s-lim}_{t\to\pm\infty}\exp\{if(H,t)\}Q(\varphi,t)$, where $Q$ is a certain operator constructed explicitly from $\Lambda$ and $f$, is independent of the choice of $f$ and is identical with $W_{\pm}(H,H_0|\Lambda)$. In some cases the invariance
principle can be justified by invoking a theorem proved in the paper. Applications
of this theorem to the Schrödinger equation are considered.
Received: 26.10.1970
Citation:
V. B. Matveev, “Invariance principle for generalized wave operators”, TMF, 8:1 (1971), 49–54; Theoret. and Math. Phys., 8:1 (1971), 663–667
Linking options:
https://www.mathnet.ru/eng/tmf4357 https://www.mathnet.ru/eng/tmf/v8/i1/p49
|
Statistics & downloads: |
Abstract page: | 320 | Full-text PDF : | 90 | References: | 39 | First page: | 1 |
|