Practical Stabilization of a Quantum Particle in a One-Dimensional Infinite Square Potential Well

We consider a nonrelativistic charged particle in a one-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time-depending electric field. It is represented by a complex probability amplitude solution of a Schrodinger equation on a one-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global practical stabilization of the eigenstates by explicit feedback laws.

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