2020/12/31 by M. Alkhateeb, X. Gutierrez de la Cal, M. Pons +2 · 1 citation
Physics and Astronomy · #quant-ph #hep-th
paper · pdf · doi:10.1103/physreva.103.042203
published as Phys. Rev. A 103, 042203 (2021) · Some text moved from main body to Appendices; close to published version
arxiv created 2021/03/22 · arxiv updated 2021/04/14
We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of the usual connection formulas for the scattering basis functions. In a time-dependent formulation, the divergent character of the MSE naturally accounts for charge creation at the barrier boundaries. In the Dirac case, the MSE converges and no charge is created. We show that this time-dependent charge behavior dynamics can adequately explain the Klein paradox in a first quantized setting. We further compare our semi-analytical wavepacket approach to exact finite-difference solutions of the relativistic wave equations.