Finite Difference Approximation of Control Via the Potential in a 1-D Schrodinger Equation
Date
2000-04-12
Authors
Kime, Katherine
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Crank-Nicolson, Potential barrier, Control, Maple
Citation
Kime, K. (2000). Finite difference approximation of control via the potential in a 1-D Schrodinger equation. <i>Electronic Journal of Differential Equations, 2000</i>(26), pp. 1-10.
Rights
Attribution 4.0 International