论文标题
狄拉克无法穿透的屏障在克莱因能量区的极限点
The Dirac impenetrable barrier in the limit point of the Klein energy zone
论文作者
论文摘要
我们重新分析了一个1D狄拉克单个粒子与高度$ v_ {0} $相撞的1D单个粒子的问题，并具有积极的传入能量，趋向于所谓的Klein klein Energy Zone的极限，即$ e \ rightArrow v_ \ rightArrow v_ {0} {0} - \ Mathrm {mathrm {m} c^$ v_ {0} $ v_ {0} $ {2} $ {2} $ {2} $ {2} $ {2} $ {2} $。在这种情况下，粒子实际上与坚不可摧的屏障相撞。实际上，对于给定的相对论能量$ e \，（<v_ {0}）$，$ v_ {0} \ rightArrow e+\ mathrm {m} c^{2} $是步骤的最大值，并且确保了障碍物的完美性能。然而，我们注意到，与非依赖性情况不同，在障碍物或步骤下的区域中，整个特征溶液并不完全消失，但是其上部分确实满足了屏障处的dirichlet边界条件。更重要的是，通过计算该本征态粒子上无法穿透的壁施加的力的平均值并采取其非依赖性极限，我们恢复了所需的结果。我们使用两种不同的方法来获得后两个结果。在这些方法之一中，粒子上的相应力是一种边界量子力。在整个文章中，还讨论了与Klein能量区有关的各种问题，该问题的解决方案以及与边界条件相关的坚不可摧的障碍。特别是，如果使用了负能传输的解决方案，则散射解决方案的较低组件满足了障碍物的差异边界条件，但是当$ v_ {0} \ rightArrow e+\ mathrm {m} c^{2} $时，外部力的平均值似乎与存在的brarrieremeremere的存在似乎并不兼容。
We reanalyze the problem of a 1D Dirac single particle colliding with the electrostatic potential step of height $V_{0}$ with a positive incoming energy that tends to the limit point of the so-called Klein energy zone, i.e., $E\rightarrow V_{0}-\mathrm{m}c^{2}$, for a given $V_{0}$. In such a case, the particle is actually colliding with an impenetrable barrier. In fact, $V_{0}\rightarrow E+\mathrm{m}c^{2}$, for a given relativistic energy $E\,(<V_{0})$, is the maximum value that the height of the step can reach and that ensures the perfect impenetrability of the barrier. Nevertheless, we note that, unlike the nonrelativistic case, the entire eigensolution does not completely vanish, either at the barrier or in the region under the step, but its upper component does satisfy the Dirichlet boundary condition at the barrier. More importantly, by calculating the mean value of the force exerted by the impenetrable wall on the particle in this eigenstate and taking its nonrelativistic limit, we recover the required result. We use two different approaches to obtain the latter two results. In one of these approaches, the corresponding force on the particle is a type of boundary quantum force. Throughout the article, various issues related to the Klein energy zone, the transmitted solutions to this problem, and impenetrable barriers related to boundary conditions are also discussed. In particular, if the negative-energy transmitted solution is used, the lower component of the scattering solution satisfies the Dirichlet boundary condition at the barrier, but the mean value of the external force when $V_{0}\rightarrow E+\mathrm{m}c^{2}$ does not seem to be compatible with the existence of the impenetrable barrier.
