  This paper provides the long-missing foundation to connect semiconductor and
atomic notations and to support results incorrectly obtained by doing as if
semiconductor electrons possessed an orbital angular momentum. We here show
that the phase factor between valence-electron destruction operator and hole
creation operator is the same as the one between particle and antiparticle in
quantum relativity, namely $\hat{a}_{m}=(-1)^{j-m} \hat{b}^\dag_{-m}$ provided
that $m=(j,j-1\cdots,-j)$ labels the degenerate states of the $(2j+1)$-fold
electron level at hand. This result is remarkable because $(i)$ the hole is
definitely not a naive antiparticle due to the remaining valence electrons;
$(ii)$ unlike atomic electrons in a central potential, semiconductor electrons
in a periodic crystal do not have orbital angular momentum
$\textbf{L}=\textbf{r}\wedge\textbf{p}$ nor angular momentum
$\textbf{J}=\textbf{L}+\textbf{S}$. Consequently, $(j,m)$ for semiconductor
electrons merely are convenient notations to label the states of a degenerate
level. To illustrate the physical implications, we discuss the interband
couplings between photons and semiconductor, in terms of valence electrons and
of holes: the phase factor is crucial to establish that bright excitons are in
a spin-singlet state.
