### 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 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 language | English |
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Pages (from-to) | 519-533 |

Number of pages | 15 |

Journal | Mathematical and Computer Modelling |

Volume | 40 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 2004 Sep 1 |

### Keywords

- 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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## Cite this

*Mathematical and Computer Modelling*,

*40*(5-6), 519-533. https://doi.org/10.1016/j.mcm.2003.11.006