TY - JOUR
T1 - Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems
AU - Hwang, Tsung Min
AU - Wang, Wei Cheng
AU - Wang, Weichung
N1 - Funding Information:
We are grateful to Wen-Wei Lin and Yin-Liang Huang for many helpful discussions with them and to Yi-Hsien Liu for assistance in some programming efforts and computational results. We are also grateful to the referees for their valuable suggestions and comments. This work is partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan.
PY - 2007/9/10
Y1 - 2007/9/10
N2 - In this article, we present efficient and stable numerical schemes to simulate three-dimensional quantum dot with irregular shape, so that we can compute all the bound state energies and associated wave functions. A curvilinear coordinate system that fits the target quantum dot shape is first determined. Three finite difference discretizations of the Schrödinger equation are then developed on the original and the skewed curvilinear coordinate system. The resulting large-scale generalized eigenvalue systems are solved by a modified Jacobi-Davidson method. Intensive numerical experiments show that the scheme using both grid points on the original and skewed curvilinear coordinate system can converge to the eigenpairs quickly and stably with second-order accuracy.
AB - In this article, we present efficient and stable numerical schemes to simulate three-dimensional quantum dot with irregular shape, so that we can compute all the bound state energies and associated wave functions. A curvilinear coordinate system that fits the target quantum dot shape is first determined. Three finite difference discretizations of the Schrödinger equation are then developed on the original and the skewed curvilinear coordinate system. The resulting large-scale generalized eigenvalue systems are solved by a modified Jacobi-Davidson method. Intensive numerical experiments show that the scheme using both grid points on the original and skewed curvilinear coordinate system can converge to the eigenpairs quickly and stably with second-order accuracy.
KW - Bound state energies and wave functions
KW - Curvilinear coordinate system
KW - Finite difference
KW - Large-scale generalized eigenvalue problem
KW - The Schrödinger equation
KW - Three-dimensional irregular shape quantum dot
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U2 - 10.1016/j.jcp.2007.04.022
DO - 10.1016/j.jcp.2007.04.022
M3 - Article
AN - SCOPUS:34548424467
SN - 0021-9991
VL - 226
SP - 754
EP - 773
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 1
ER -