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

Tsung Min Hwang, Wei Cheng Wang, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)754-773
Number of pages20
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 2007 Sept 10


  • Bound state energies and wave functions
  • Curvilinear coordinate system
  • Finite difference
  • Large-scale generalized eigenvalue problem
  • The Schrödinger equation
  • Three-dimensional irregular shape quantum dot

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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