  We derive the minimal Fock-state expansions of the pion and the photon wave
functions in light-cone formalism, then we calculate the pion-photon and the
photon-pion transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma $ and
$\gamma ^{\ast}\gamma \to \pi ^{0}$ processes by employing these
quark-antiquark wave functions of the pion and the photon. We find that our
calculation for the $\gamma ^{\ast}\gamma \to \pi ^{0}$ transition form factor
agrees with the experimental data at low and moderately high energy scale.
Moreover, the physical differences and inherent connections between the
transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma $ and $ \gamma
^{\ast}\gamma \to \pi ^{0}$ have been illustrated, which indicate that these
two physical processes are intrinsically related. In addition, we also discuss
the $\pi ^{0}\to \gamma \gamma $ form factor and the decay width $
\mathit{\Gamma}(\pi \to \gamma \gamma)$ at $Q^{2}=0$.
