Numerical approximation of bilinear control of the schroedinger equation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish (US)
Title of host publicationProc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005
Subtitle of host publication5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Pages623-626
Number of pages4
StatePublished - Dec 1 2005
EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States
Duration: Sep 24 2005Sep 28 2005

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume6 A

Conference

ConferenceDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CityLong Beach, CA
Period9/24/059/28/05

Fingerprint

MATLAB

Keywords

  • Control
  • MATLAB
  • Numerical
  • Potential
  • Schroedinger

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Kime, K. A. (2005). Numerical approximation of bilinear control of the schroedinger equation. In Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (pp. 623-626). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 6 A).

Numerical approximation of bilinear control of the schroedinger equation. / Kime, Katherine A.

Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. 2005. p. 623-626 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 6 A).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kime, KA 2005, Numerical approximation of bilinear control of the schroedinger equation. in Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005, vol. 6 A, pp. 623-626, DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, United States, 9/24/05.
Kime KA. Numerical approximation of bilinear control of the schroedinger equation. In Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. 2005. p. 623-626. (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005).
Kime, Katherine A. / Numerical approximation of bilinear control of the schroedinger equation. Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. 2005. pp. 623-626 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005).
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