| Volume 6, Number 3, 2016, Pages 851-864 DOI：10.11948/2016054 |
| Local exact controllability of Schr\"{o}dinger equation with Sturm- Liouville boundary value problems |
| Jian Zu,Yong Li |
| Keywords:Controllability, Bilinear Schr\"{o}dinger equation, Sturm-Liouville boundary value condition. |
| 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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