We construct the most general families of self-adjoint boundary conditions for three (equivalent) Weyl Hamiltonian operators, each describing a three-dimensional Weyl particle in a one-dimensional box situated along a Cartesian axis. These results are essentially obtained by using the most general family of self-adjoint boundary conditions for a Dirac Hamiltonian operator that describes a one-dimensional Dirac particle in a box, in the Weyl representation, and by applying simple changes of representation to this operator. Likewise, we present the most general family of self-adjoint boundary conditions for a Weyl Hamiltonian operator that describes a one-dimensional Weyl particle in a one-dimensional box. We also obtain and discuss throughout the article distinct results related to the Weyl equations in (3+1) and (1+1) dimensions, in addition to their respective wave functions, and present certain key results related to representations for the Dirac equation in (1+1) dimensions.

我们为三个（等效）Weyl Hamiltonian算子构造了最一般的自伴随边界条件族，每个算子在沿笛卡尔轴定位的一维框中描述了三维Weyl粒子。这些结果基本上是通过使用最普遍的Dirac哈密顿算子的自伴边界条件族获得的，该算子在Weyl表示中描述了框中的一维Dirac粒子，并对该表示进行了简单的表示更改。同样，我们介绍了Weyl Hamiltonian算子的最一般的自伴边界条件，该算子描述了一维盒子中的一维Weyl粒子。我们还将在整篇文章中获得并讨论与（3 + 1）和（1 + 1）维中的Weyl方程有关的不同结果，