Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6932820 | Journal of Computational Physics | 2014 | 18 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Martin Almquist, Ken Mattsson, Tomas Edvinsson,