High-fidelity numerical solution of the time-dependent Dirac equation
- Uppsala University, Department of Information Technology, Lägerhyddsvägen 2, 752 37 Uppsala (Sweden)
- Uppsala University, Department of Chemistry – Ångström Laboratory, Lägerhyddsvägen 1, 751 21 Uppsala (Sweden)
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.
- OSTI ID:
- 22314854
- Journal Information:
- Journal of Computational Physics, Vol. 262; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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