3. Methods for Band Structure Calculations in Solids

  • A. Ernst
  • M. Lüders
Part I Basic Description of Electrons and Photons in Crystals
Part of the Lecture Notes in Physics book series (LNP, volume 642)


The calculation of the ground-state and excited-state properties of materials is one of the main goals of condensed matter physics. While the most successful first-principles method, the density-functional theory (DFT), provides, in principle, the exact ground-state properties, the many-body method is the most suitable approach for studying excited-state properties of extended systems. Here we discuss general aspects of the Green’s function and different approximations for the self-energy to solve the Dyson equation. Further we present some tools for solving the Dyson equation with several approximations for the self-energy: a highly precise combined basis method providing the band structure in the Kohn-Sham approximation, and some implementations for the random-phase approximation.


Plane Wave Dyson Equation LMTO Method Linearise Augmented Plane Wave Method Exact Ground State Energy 
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Authors and Affiliations

  • A. Ernst
    • 1
  • M. Lüders
    • 2
  1. 1.Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 HalleGermany
  2. 2.Daresbury Laboratory, Warrington WA4 4ADUnited Kingdom

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