  In (1+1) space-time dimensions, we can have two particles that are Weyl and
Majorana particles at the same time---1D Weyl-Majorana particles. That is, the
right-chiral and left-chiral parts of the two-component Dirac wave function
that satisfies the Majorana condition, in the Weyl representation, describe
these particles, and each satisfies their own Majorana condition. Naturally,
the nonzero component of each of these two two-component wave functions
satisfies a Weyl equation. We investigate and discuss this issue and
demonstrate that for a 1D Weyl-Majorana particle in a box, the nonzero
components, and therefore the chiral wave functions, only admit the periodic
and antiperiodic boundary conditions. From the latter two boundary conditions,
we can only construct four boundary conditions for the entire Dirac wave
function. Then, we demonstrate that these four boundary conditions are also
included within the most general set of self-adjoint boundary conditions for a
1D Majorana particle in a box.
