Useful Procedure for Computing the Lattice Green's Function-Square, Tetragonal, and bcc Lattices
- 1 August 1971
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (8) , 1744-1747
- https://doi.org/10.1063/1.1665800
Abstract
A recurrence relation, which gives the values of the lattice Green's function along the diagonal direction from a couple of the elliptic integrals of the first and second kind, is derived for the square lattice by an elementary partial integration. The values of the square lattice Green's function at an arbitrary site are then calculated in a successive way with the aid of the difference equation defining the function. Discussions are given of the application of this result to the calculation of the lattice Green's function of the tetragonal and body-centered cubic lattices.Keywords
This publication has 3 references indexed in Scilit:
- Lattice Green's Functions for the Rectangular and the Square Lattices at Arbitrary PointsJournal of Mathematical Physics, 1971
- Lattice Green's Function for the Simple Cubic LatticeJournal of the Physics Society Japan, 1971
- Numerical calculation of elliptic integrals and elliptic functionsNumerische Mathematik, 1965