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

Karine Beauchard; Mazyar Mirrahimi

doi:10.1137/070704204

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

Karine Beauchard
, Mazyar Mirrahimi

Research output: Contribution to journal › Article › peer-review

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 Schrödinger 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.

Original language	English
Pages (from-to)	1179-1205
Number of pages	27
Journal	SIAM Journal on Control and Optimization
Volume	48
Issue number	2
DOIs	https://doi.org/10.1137/070704204
Publication status	Published - 1 Dec 2009
Externally published	Yes

Keywords

Bilinear schrödinger equation
Control of partial differential equations
Lyapunov stabilization
Quantum systems

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10.1137/070704204

Cite this

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AB - 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 Schrödinger 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.

KW - Bilinear schrödinger equation

KW - Control of partial differential equations

KW - Lyapunov stabilization

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

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Keywords

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