MATHEMATICS COLLOQUIUM

 WHEN:
On Thursday, March 23, 2000 at 2:20 PM

WHERE:
Durham Science Center, Room 255

WHAT:

Katherine Kime
Department of Mathematics and Statistics
University of Nebraska at Kearney

will give a talk on

Applying Existing Numerical Methods to Control of Nanostructures

Abstract:
We consider numerical approximation of the time-dependent Schrodinger equation with a time-dependent potential, the control. An important question in control theory of differential equations is the characterization of accessible states; given initial and terminal data, can one choose a term, the control, in a differential equation which "steers" the initial data to the terminal data? We discuss this question for the Schrodinger equation, and give a condition for existence of a control within our approximation and some numerical examples. Potential barriers and wells are basic examples arising in quantum systems, among them nanostructures, which are of increasing interest. The control of nanostructures is yet to be fully understood. The set-up we discuss can be seen as a precursor to more complicated situations, and is itself sufficiently complex that the computer algebra system Maple is of significant aid.