  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.
