Control of matter waves in adjacent potential wells

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Abstract

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 languageEnglish (US)
Pages (from-to)369-381
Number of pages13
JournalMathematical Methods in the Applied Sciences
Volume20
Issue number4
DOIs
StatePublished - Mar 10 1997

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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