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Fixed-point methods for a semiconductor quantum dot model. (English) Zbl 1112.82331

Summary: 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.

MSC:

82D37 Statistical mechanics of semiconductors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Software:

LAPACK; JDQZ; JDQR
PDFBibTeX XMLCite
Full Text: DOI

References:

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