We consider exact controllability of a system of two Schrödinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant V0. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hubert uniqueness method is used to obtain the exact controllability result. If K0 is sufficiently small, there exists a time T̂(V0) such that the system is exactly controllable in times T > T̂(V0).
|Original language||English (US)|
|Number of pages||13|
|Journal||Mathematical Methods in the Applied Sciences|
|State||Published - Mar 10 1997|
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