论文标题
关于一维主要粒子的狄拉克方程的真实溶液
On real solutions of the Dirac equation for a one-dimensional Majorana particle
论文作者
论文摘要
我们在Majorana表示中构建了具有Lorentz标量势的（1+1）维度的（1+1）维度的一般解。在这种情况下，这些解决方案是实现的，并描述了一维主要的单个粒子。我们明确地获得了以下情况的解决方案：盒子内的静止粒子，一个自由的（即，在具有周期性边界条件的可穿透盒中），在无电势的难以穿透的盒子中（这里我们只有四个边界条件），并且具有线性电势。所有这些问题都是以非常详细和系统的方式处理的。此外，我们获得并讨论与真实波函数相关的各种结果。最后，我们还希望指出，在选择Majorana表示时，可以选择具有Lorentz标量电势的Dirac方程的解决方案是真实的，但不需要真实。实际上，也可以获得该方程式的复杂解决方案。因此，仅在Majorana代表中的DIRAC方程中不能描述一个Majorana粒子，而不会明确施加Majoraana条件。
We construct general solutions of the time-dependent Dirac equation in (1+1) dimensions with a Lorentz scalar potential, subject to the so-called Majorana condition, in the Majorana representation. In this situation, these solutions are real-valued and describe a one-dimensional Majorana single particle. We specifically obtain solutions for the following cases: a Majorana particle at rest inside a box, a free (i.e., in a penetrable box with the periodic boundary condition), in an impenetrable box with no potential (here we only have four boundary conditions), and in a linear potential. All these problems are treated in a very detailed and systematic way. In addition, we obtain and discuss various results related to real wave functions. Finally, we also wish to point out that, in choosing the Majorana representation, the solutions of the Dirac equation with a Lorentz scalar potential can be chosen to be real but do not need to be real. In fact, complex solutions for this equation can also be obtained. Thus, a Majorana particle cannot be described only with the Dirac equation in the Majorana representation without explicitly imposing the Majorana condition.
