Local controllability of a 1-D Schrödinger equation

Abstract We consider a nonrelativistic charged particle in a 1-D box of potential. This quantum system is subject to a control, which is a uniform electric field. It is represented by a complex probability amplitude solution of a Schrodinger equation. We prove the local controllability of this nonlinear system around the ground state. Our proof uses the return method, a Nash–Moser implicit function theorem and moment theory.

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