论文标题
对大规模颗粒及其在量子隧道中的应用的变性解决方案
Degenerate solutions to the Dirac equation for massive particles and their applications in quantum tunneling
论文作者
论文摘要
在最近的一项工作中，我们证明了对狄拉克方程的退化解决方案的存在，与无限数量的不同电磁场相对应，还提供了有关无质量颗粒的一些例子。在本文中，我们的结果显着扩展，为具有任意质量的颗粒提供了dirac方程的脱同个溶液，在某些条件下，可以将其解释为成对的颗粒（或反粒子）成对的潜在屏障，其能量等于屏障高度，并相互旋转。我们计算与这些溶液相对应的电磁场，还提供了一些有关空间恒定电磁场和电磁波的示例。此外，我们讨论了我们工作的一些潜在应用，主要是关于对潜在屏障以外的颗粒的控制，而不会影响其在障碍物内的状态。最后，我们研究了小扰动对退化溶液的影响，这表明我们的结果在近似意义上仍然有效，只要与确切的退化溶液相对应的电磁场的幅度足够小。
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present article our results are extended significantly, providing degenerate solutions to the Dirac equation for particles with arbitrary mass, which, under certain conditions, could be interpreted as pairs of particles (or antiparticles) moving in a potential barrier with energy equal to the height of the barrier and spin opposite to each other. We calculate the electromagnetic fields corresponding to these solutions, providing also some examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, we discuss some potential applications of our work, mainly regarding the control of the particles outside the potential barrier, without affecting their state inside the barrier. Finally, we study the effect of small perturbations to the degenerate solutions, showing that our results are still valid, in an approximate sense, provided that the amplitude of the electromagnetic fields corresponding to the exact degenerate solutions is sufficiently small.
