Electron. J. Diff. Eqns., Vol. 2000(2000), No. 26, pp. 1-10.

Finite difference approximation of control via the potential in a 1-D Schrodinger equation

K. Kime

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.

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Katherine Kime
Dept. of Mathematics and Statistics
Univ. of Nebraska at Kearney
Kearney, NE 68849 USA
email: kimek@unk.edu

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