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Title: High-fidelity numerical solution of the time-dependent Dirac equation

A stable high-order accurate finite difference method for the time-dependent Dirac equation is derived. Grid-convergence studies in 1-D and 3-D corroborate the analysis. The method is applied to time-resolved quantum tunneling where a comparison with the solution to the time-dependent Schrödinger equation in 1-D illustrates the differences between the two equations. In contrast to the conventional tunneling probability decay predicted by the Schrödinger equation, the Dirac equation exhibits Klein tunneling. Solving the time-dependent Dirac equation with a step potential in 3-D reveals that particle spin affects the tunneling process. The observed spin-dependent reflection allows for a new type of spin-selective measurements.
Authors:
 [1] ;  [1] ;  [2]
  1. Uppsala University, Department of Information Technology, Lägerhyddsvägen 2, 752 37 Uppsala (Sweden)
  2. Uppsala University, Department of Chemistry – Ångström Laboratory, Lägerhyddsvägen 1, 751 21 Uppsala (Sweden)
Publication Date:
OSTI Identifier:
22314854
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 262; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; CONVERGENCE; DIRAC EQUATION; FINITE DIFFERENCE METHOD; MATHEMATICAL SOLUTIONS; POTENTIALS; PROBABILITY; REFLECTION; SCHROEDINGER EQUATION; SPIN; TIME DEPENDENCE; TIME RESOLUTION; TUNNEL EFFECT