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Practical stabilization of a quantum particle in a one-dimensional infinite square potential well

Abstract : 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) timedepending electric field. It is represented by a complex probability amplitude solution of a Schr¨odinger 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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https://hal.inria.fr/hal-00793356
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Submitted on : Friday, February 22, 2013 - 10:54:37 AM
Last modification on : Friday, January 21, 2022 - 3:13:44 AM

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Karine Beauchard, Mazyar Mirrahimi. Practical stabilization of a quantum particle in a one-dimensional infinite square potential well. SIAM Journal on Control and Optimization, 2009, 48 (2), pp.1179-1205. ⟨10.1137/070704204⟩. ⟨hal-00793356⟩

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