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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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2009, 48 (2), pp.1179-1205. 〈10.1137/070704204〉
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Soumis le : vendredi 22 février 2013 - 10:54:37
Dernière modification le : mardi 17 avril 2018 - 11:34:39

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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, Society for Industrial and Applied Mathematics, 2009, 48 (2), pp.1179-1205. 〈10.1137/070704204〉. 〈hal-00793356〉

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