  It is known that the $2+1$d single Majorana fermion theory has an anomaly of
the reflection, which is canceled out when 16 copies of the theory are
combined. Therefore, it is expected that the reflection symmetric boundary
condition is impossible for one Majorana fermion, but possible for 16 Majorana
fermions. In this paper, we consider a reflection symmetric boundary condition
that varies at a single point, and find that there is a problem with one
Majorana fermion. The problem is the absence of a corresponding outgoing wave
to a specific incoming wave into the boundary, which leads to the
non-conservation of the energy. For 16 Majorana fermions, it is possible to
connect every incoming wave to an outgoing wave without breaking the reflection
symmetry. In addition, we discuss the connection with the fermion-monopole
scattering in $3+1$ dimensions.
