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Title: Sinc-based method for an efficient solution in the direct space of quantum wave equations with periodic boundary conditions

The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually involve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
Authors:
; ;  [1]
  1. Dipartimento di Ingegneria dell'Informazione, Università di Pisa, Via Caruso 16, I-56122 Pisa (Italy)
Publication Date:
OSTI Identifier:
22224095
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 114; Journal Issue: 17; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ACCURACY; BOUNDARY CONDITIONS; DIRAC EQUATION; FINITE DIFFERENCE METHOD; FOURIER TRANSFORMATION; GRAPHENE; NANOSTRUCTURES; PERIODICITY; SPACE