  We study excitations of atomic vibrations in the reciprocal space for
amorphous solids. There are two kinds of excitations we obtained, collective
excitation and local excitation. The collective excitation is the collective
vibration of atoms in the amorphous solids while the local excitation is
stimulated locally by a single atom vibrating in the solids. We introduce a
continuous wave vector for the study and transform the equations of atomic
vibrations from the real space to the reciprocal space. We take the amorphous
silicon as an example and calculate the structures of the excitations in the
reciprocal space. Results show that an excitation is a wave packet composed of
a collection of plane waves. We also find a periodical structure in the
reciprocal space for the collective excitation with longitudinal vibrations,
which is originated from the local order of the structure in the real space of
the amorphous solid.
