TY - JOUR
T1 - A finite-difference method for the one-dimensional time-dependent schrödinger equation on unbounded domain
AU - Han, Houde
AU - Jin, Jicheng
AU - Wu, Xiaonan
N1 - Funding Information:
*The research is partly supported by the Special Funds for Major State Basic Research Projects of China. t Author to whom all correspondence should be addressed. SThe research is supported by RCC of Hong Kong and FRG of Hong Kong Baptist University. The authors wish to thank the referees for many valuable suggestions.
PY - 2005/10
Y1 - 2005/10
N2 - A finite-difference scheme is proposed for the one-dimensional time-dependent Schrödinger equation. We introduce an artificial boundary condition to reduce the original problem into an initial-boundary value problem in a finite-computational domain, and then construct a finite-difference scheme by the method of reduction of order to solve this reduced problem. This scheme has been proved to be uniquely solvable, unconditionally stable, and convergent. Some numerical examples are given to show the effectiveness of the scheme.
AB - A finite-difference scheme is proposed for the one-dimensional time-dependent Schrödinger equation. We introduce an artificial boundary condition to reduce the original problem into an initial-boundary value problem in a finite-computational domain, and then construct a finite-difference scheme by the method of reduction of order to solve this reduced problem. This scheme has been proved to be uniquely solvable, unconditionally stable, and convergent. Some numerical examples are given to show the effectiveness of the scheme.
KW - Artificial boundary conditions
KW - Finite-difference method
KW - The Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=28844493429&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2005.05.006
DO - 10.1016/j.camwa.2005.05.006
M3 - Journal article
AN - SCOPUS:28844493429
SN - 0898-1221
VL - 50
SP - 1345
EP - 1362
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 8-9
ER -