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V. I. Smirnov Seminar on Mathematical Physics
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On the rate of decrease at infinity for solutions to the Schrödinger equation in a half-cylinder (on a joint research with S.Krymskii) N. D. Filonov St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences |
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Abstract: We consider the equation $$ -\Delta u + V u = 0 $$ in the half-cylinder $$ u (x,y) = O \left(e^{-Nx}\right) \quad \forall \ N, $$ then $$ u (x,y) = O \left(e^{-Nx^{4/3}}\right) \quad \forall \ N \qquad \Longrightarrow \qquad u \equiv 0. $$ |