Geodesic
Finite difference approximation of control via the potential in a 1-D Schrödinger equation
Electronic Journal of Differential Equations, Tome 2000 (2000), pp. 1-10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 81Q05, 93C20
Keywords: Crank-Nicolson, potential barrier, control, Maple 
@article{EJDE_2000__2000__a94,
     author = {Kime, K.},
     title = {Finite difference approximation of control via the potential in a {1-D} {Schr\"odinger} equation},
     journal = {Electronic Journal of Differential Equations},
     pages = {1--10},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/}
}
TY  - JOUR
AU  - Kime, K.
TI  - Finite difference approximation of control via the potential in a 1-D Schrödinger equation
JO  - Electronic Journal of Differential Equations
PY  - 2000
SP  - 1
EP  - 10
VL  - 2000
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/
LA  - en
ID  - EJDE_2000__2000__a94
ER  - 
%0 Journal Article
%A Kime, K.
%T Finite difference approximation of control via the potential in a 1-D Schrödinger equation
%J Electronic Journal of Differential Equations
%D 2000
%P 1-10
%V 2000
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/
%G en
%F EJDE_2000__2000__a94
Kime, K. Finite difference approximation of control via the potential in a 1-D Schrödinger equation. Electronic Journal of Differential Equations, Tome 2000 (2000), pp. 1-10. http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/