Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems

Tsung Min Hwang, Wei Cheng Wang, Weichung Wang

研究成果: 雜誌貢獻文章

11 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)754-773
頁數20
期刊Journal of Computational Physics
226
發行號1
DOIs
出版狀態已發佈 - 2007 九月 10

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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