2009/04/03 by Jihad Asad, J. H. Asad, Asad, J. H.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #General Physics (physics.gen-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0904.0511
24 pages, 13 figures
arxiv created 2009/04/03 · openalex publication_date 2009/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's Function at the site (m,n)and the first derivative of the lattice Green's Function at the site (m+1,n)is presented for the two- dimensional lattice, a differential equation of the second order in G(0,0) is obtained. By making use of the letter recurrence relation, lattice Green's Function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross section are evaluated analytically and numerically for one- and two impurities.