AbstractIn this note the three dimensional Dirac operator $$A_m$$
A
m
with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $$A_m$$
A
m
is self-adjoint in $$L^2(\Omega ;{\mathbb {C}}^4)$$
L
2
(
Ω
;
C
4
)
for any open set $$\Omega \subset {\mathbb {R}}^3$$
Ω
⊂
R
3
and its spectrum is described explicitly in terms of the spectrum of the Dirichlet Laplacian in $$\Omega $$
Ω
. In particular, whenever the spectrum of the Dirichlet Laplacian is purely discrete, then also the spectrum of $$A_m$$
A
m
consists of discrete eigenvalues that accumulate at $$\pm \infty $$
±
∞
and one additional eigenvalue of infinite multiplicity.
Spectrum of the periodic Dirac operator