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
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},
     year = {2000},
     volume = {2000},
     zbl = {1040.81011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/}
}
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VL  - 2000
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a94/
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%J Electronic journal of differential equations
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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/