  We investigate the dynamics of electrons in the vicinity of the Anderson
transition in $d=3$ dimensions. Using the exact eigenstates from a numerical
diagonalization, a number of quantities related to the critical behavior of the
diffusion function are obtained. The relation $\eta = d-D_{2}$ between the
correlation dimension $D_{2}$ of the multifractal eigenstates and the exponent
$\eta$ which enters into correlation functions is verified. Numerically, we
have $\eta\approx 1.3$. Implications of critical dynamics for experiments are
predicted. We investigate the long-time behavior of the motion of a wave
packet. Furthermore, electron-electron and electron-phonon scattering rates are
calculated. For the latter, we predict a change of the temperature dependence
for low $T$ due to $\eta$. The electron-electron scattering rate is found to be
linear in $T$ and depends on the dimensionless conductance at the critical
point.
