Local exact controllability of Schr"{o}dinger equation with Sturm- Liouville boundary value problems |
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| Authors: | Jian Zu and Yong Li |
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| Affiliation: | School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, 130024 Changchun, P.R. China;Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, 2555 Jingyue Street, 130117 Changchun, P.R. China and School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, 130024 Changchun, P.R. China;Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, 2555 Jingyue Street, 130117 Changchun, P.R. China |
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| Abstract: | In this paper, we investigate the controllability of 1D bilinear Schr"{o}dinger equation with Sturm-Liouville boundary value condition. The system represents a quantumn particle controlled by an electric field. K. Beauchard and C. Laurent have proved local controllability of 1D bilinear Schr"{o}dinger equation with Dirichlet boundary value condition in some suitable Sobolev space based on the classical inverse mapping theorem. Using a similar method, we extend this result to Sturm-Liouville boundary value proplems. |
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| Keywords: | Controllability, Bilinear Schr" {o}dinger equation, Sturm-Liouville boundary value condition. |
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