Fixed-point methods for a semiconductor quantum dot model

Tsung Min Hwang, Wen Wei Lin, Jinn Liang Liu, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper presents various fixed-point methods for computing the ground state energy and its associated wave function of a semiconductor quantum dot model. The discretization of the three-dimensional Schrödinger equation leads to a large-scale cubic matrix polynomial eigenvalue problem for which the desired eigenvalue is embedded in the interior of the spectrum. The cubic problem is reformulated in several forms so that the desired eigenpair becomes a fixed point of the new formulations. Several algorithms are then proposed for solving the fixed-point problem. Numerical results show that the simple fixed-point method with acceleration schemes can be very efficient and stable.

Original languageEnglish
Pages (from-to)519-533
Number of pages15
JournalMathematical and Computer Modelling
Issue number5-6
Publication statusPublished - 2004 Sept


  • 3D Schrödinger equation
  • Cubic eigenvalue problem
  • Fixed-point method
  • Linear Jacobi-Davidson method
  • Linear successive iterations

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications


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