### Abstract

The need to calculate the spectral properties of a Hermitian operator H frequently arises in the technical sciences. A common approach to its solution in volves the construction of the Green's function operator G(z) = [z - H]^{-1} in the complex z plane. For example, the energy spectrum and other physical properties of condensed matter systems can often be elegantly and naturally expressed in terms of the Kohn-Sham Green's functions. However, the nonanalyticity of resolvents on the real axis makes them difficult to compute and manipulate. The Herglotz property of a Green's function allows one to calculate it along an arc with a small but finite imaginary part, i.e., G(x + iy), and then to continue it to the real axis to determine quantities of physical interest. In the past, finite-difference techniques have been used for this continuation. We present here a fundamentally new algorithm based on the fast Fourier transform which is both simpler and more effective.

Original language | English (US) |
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Pages (from-to) | 99-108 |

Number of pages | 10 |

Journal | Journal of Computational Physics |

Volume | 126 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computational Physics*,

*126*(1), 99-108. https://doi.org/10.1006/jcph.1996.0123