  In the paper, we have given the quantum transmissivity, probability density
and probability current density of photon in one-dimensional photonic crystals
$(AB)^N$ with the quantum theory approach. We find the quantum transmissivity
is identical to the classical transmissivity. When the incident angle $\theta$
and periodic number $N$ change the probability density and probability current
density are approximate periodic change, and their amplitude are increased with
the incident angles $\theta$ and periodic number $N$ increasing. Otherwise, we
find when the frequency of incident photon is corresponding to transmissivity
$T=1$, the amplitude of the probability density is the largest. When the
frequency of incident photon is corresponding to transmissivity $T=0$, the
amplitude of the probability density attenuate rapidly to zero, it indicates
that there is the quantum tunnel effect of photon in photonic crystals.
