Fixed-point methods for asemiconductor quantum dot model

  • Authors:

  • Tsung-Min Hwang;Wen-Wei Lin;Jinn-Liang Liu;Weichung Wang

  • Affiliations:

  • Department of Mathematics, National Taiwan Normal University Taipei 116, Taiwan, R.O.C.;Department of Mathematics, National Tsing Hua University Hsinchu 300, Taiwan, R.O.C.;Department of Applied Mathematics, National Chiao Tung UniversityHsinchu 300, Taiwan, R.O.C.;Department of Applied Mathematics, National University of KaohsiungKaohsiung 811, Taiwan, R.O.C.

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2004

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Abstract

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 Schrodinger 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.