  The $\alpha$ cluster states are discussed in a model frame of extended
quantum molecular dynamics. Different alpha cluster structures are studied in
details, such as $^8$Be two-$\alpha$ cluster structure, $^{12}$C triangle
structure, $^{12}$C chain structure, $^{16}$O chain structure, $^{16}$O kite
structure, and $^{16}$O square structure. The properties studied, include as
the width of wave packets for different $\alpha$ clusters, momentum
distribution, and the binding energy among $\alpha$ clusters. It is also
discussed how the $\alpha$ cluster degree of freedom affects nuclear collective
vibrations. The cluster configurations in $^{12}$C and $^{16}$O are found to
have corresponding characteristic spectra of giant dipole resonance (GDR), and
the coherences of different $\alpha$ clusters's dipole oscillation are
described in details. The geometrical and dynamical symmetries of
$\alpha$-clustering configurations are responsible for the number and centroid
energies of peaks of GDR spectra. Therefore, the GDR can be regarded as an
effective probe to diagnose different $\alpha$ cluster configurations in light
nuclei.
