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Local controllability of a 1-D Schrödinger equation. (English) Zbl 1124.93009
Summary: 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 Schrödinger 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.

MSC:
93B05 Controllability
35Q40 PDEs in connection with quantum mechanics
81Q99 General mathematical topics and methods in quantum theory
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