@inproceedings{803c5876a36f4adf936793777cf3291b,
title = "Numerical approximation of bilinear control of the schroedinger equation",
abstract = "We consider the one-dimensional Schroedinger equation in which the control is a time-dependent rectangular potential barrier/well. This is a bilinear control problem, as the potential multiplies the state. Differential geometric methods have been used to treat the bilinear control of systems of finitely many ODEs, and have been applied to the Schroedinger equation (quantum systems). In this paper we will calculate, using MATLAB, explicit controls which steer localized initial data to localized terminal data. These will be obtained using the Crank-Nicolson approximation, in which both space and time are discretized. If one semi-discretizes, in space, one obtains a bilinear control problem for a system of finitely many ODEs. One may pass from the semi-discretized system to CrankNicolson using the trapezoid rule. Thus the controls we calculate may be used to construct approximations to controls for the system of ODEs.",
keywords = "Control, MATLAB, Numerical, Potential, Schroedinger",
author = "Kime, {Katherine A.}",
year = "2005",
doi = "10.1115/detc2005-84254",
language = "English (US)",
isbn = "0791847438",
series = "Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005",
publisher = "American Society of Mechanical Engineers",
pages = "623--626",
booktitle = "Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005",
note = "DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference ; Conference date: 24-09-2005 Through 28-09-2005",
}