Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 26, pp. 1-10.
Title: Finite difference approximation of control via the potential
in a 1-D Schrodinger equation
Author: K. Kime (Univ. of Nebraska at Kearney, NE, USA)
Abstract:
We consider the problem of steering given initial data to given
terminal data via a time-dependent potential, the control, in a 1-D
Schrodinger equation. We determine a condition for existence of a
transferring potential within our approximation. Using Maple, we give
equations for the control and also examples in which the potential is
restricted to be centralized and to be a step potential.
Submitted March 2, 2000. Published April 12, 2000.
Math Subject Classifications: 81Q05, 93C20.
Key Words: Crank-Nicolson; potential barrier; control; Maple.