SIAM Journal on Control and Optimization, Vol.48, No.2, 1179-1205, 2009
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.
Keywords:control of partial differential equations;bilinear Schrodinger equation;quantum systems;Lyapunov stabilization