Numerically Absorbing Boundary Conditions for Quantum Evolution Equations
Open Access
- 1 January 1998
- journal article
- research article
- Published by Hindawi Limited in VLSI Design
- Vol. 6 (1-4) , 313-319
- https://doi.org/10.1155/1998/38298
Abstract
Transparent boundary conditions for the transient Schrödinger equation on a domain Ω can be derived explicitly under the assumption that the given potential V is constant outside of this domain. In 1D these boundary conditions are non-local in time (of memory type). For the Crank-Nicolson finite difference scheme, discrete transparent boundary conditions are derived, and the resulting scheme is proved to be unconditionally stable. A numerical example illustrates the superiority of discrete transparent boundary conditions over existing ad-hoc discretizations of the differential transparent boundary conditions. As an application of these boundary conditions to the modeling of quantum devices, a transient 1D scattering model for mixed quantum states is presented.Keywords
Funding Information
- EC (ERBCHRXCT930413, DMS-9500852)
This publication has 0 references indexed in Scilit: