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 タイトル: Exponential Decay of Quasi-stationary States of Time-periodic Schrodinger Equation with Short Range Potentials 著者: Yajima, Kenji 発行日: 1990年 出版者: The University of Tokyo 掲載誌情報: Scientific Papers of the College of Arts and Sciences, The University of Tokyo. Vol.40(1990), Page27-36 抄録: A solution $u(t,x)\in C(R_l^1,L^2(R)_x^N))$ to a time dependent Schrodinger equation $i(\partial U/\partial t)=-\Delta u+v(t,x)u$ with time periodic potential $V(t+2\pi ,x)=V(t,x)$ is called quasi-stationary state with quasi-level λ if it satisfies $u(t-2\pi ,x)=V(t,x)=exp(-2\pi i\lambdau(t,x)$. We show, under the condition $(1+\mid x \mid )^(1+\epsilon) V(t,x)\in C^1(R_l^1,L^(\infty )(R_x^N))$, that every non-threshold quasi-stationary state decays exponentially at infinity in the sense that exp $(\alpha \mid x \mid )u(t,x)\in C^1(R_l^1,L^2(R_x^N))$ for $\alpha ^2<1-(\lambda - [\lambda ]),$ if \lambda is its quasilevel, where [\lambda ] is the integral part of \lambda . URI: http://hdl.handle.net/2261/21199 ISSN: 02897520 出現カテゴリ: Scientific Papers of the College of Arts and Sciences, The University of Tokyo Scientific Papers of the College of Arts and Sciences, The University of Tokyo

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