Differential Equation Approach for One- and Two- Dimensional Lattice Green's Function

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dc.creatorAsad, J. H.
dc.date2009-04-03
dc.date.accessioned2026-07-07T13:00:13Z
dc.date.available2026-07-07T13:00:13Z
dc.descriptionA 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.
dc.description24 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/0904.0511
dc.identifierhttp://arxiv.org/abs/0904.0511
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225786
dc.subjectGeneral Physics
dc.titleDifferential Equation Approach for One- and Two- Dimensional Lattice Green's Function
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