Interpolation and k-Space Integration: A Review

  • F. M. Mueller
Part of the The IBM Research Symposia Series book series (IRSS)


The principal techniques used to form representations of integrals over the Brillouin zone which include Dirac δ-functions in their integrands are reviewed. The problem was first solved using Monte-Carlo procedures applied directly to the Hamiltonian. Recent interest has centered on two methods which utilize microscopic interpolation. The singular integration is carried out either through Monte-Carlo procedures or through a procedure which uses a further linear expansion and numerical integration. Both of these procedures represent their results in terms of histograms. Techniques for including matrix elements in the integrand are considered and new results presented. A new technique is given which uses high order Hermite functions to numerically integrate the principal-value kernel.


Brillouin Zone Hermite Function Quadratic Interpolation Mesh Parameter Plane Wave Approximation 
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Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • F. M. Mueller
    • 1
  1. 1.Argonne National LaboratoryArgonneUSA

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