Approximate stabilization of a quantum particle in a 1D infinite square potential well
Analysis of PDEs
2008-01-11 v1
Abstract
We consider a non relativistic charged particle in a 1-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 1-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global approximate stabilization of the eigenstates by explicit feedback laws.
Cite
@article{arxiv.0801.1522,
title = {Approximate stabilization of a quantum particle in a 1D infinite square potential well},
author = {Karine Beauchard and Mazyar Mirrahimi},
journal= {arXiv preprint arXiv:0801.1522},
year = {2008}
}
Comments
26 pages, 3 figures