论文标题
Klein-Gordon和Dirac颗粒的相对论时间依赖性量子动力学
Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles
论文作者
论文摘要
我们研究了Klein-Gordon和Dirac方程的超临界障碍物的波袋动力学。我们的处理是基于多个散射扩展（MSE）。对于旋转0颗粒，MSE分解，使使用常规连接公式用于散射基函数的使用无效。在时间依赖的公式中，MSE的不同特征自然地解释了在屏障边界处的电荷创造。在狄拉克情况下，MSE收敛且无费用。我们表明，这种依赖时间的电荷行为动力学可以在第一个量化的设置中充分解释克莱因悖论。我们进一步将半分析波袋方法与相对论波方程的精确有限差解相提并论。
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.
