  Dynamical correlations of the spin and the energy density are investigated in
the critical region of the random transverse-field Ising chain by numerically
exact calculations in large finite systems (L<=128). The spin-spin
autocorrelation function is found to decay proportional to (log t)^{-2x_m} and
(log t)^{-2x_m^s} in the bulk and on the surface, respectively, with x_m and
x_m^s the bulk and surface magnetization exponents, respectively. On the other
hand the critical energy-energy autocorrelation functions have a power law
decay, which are characterized by novel critical exponents eta_e~2.2 in the
bulk and eta_e^s~2.5 at the surface, respectively. The numerical results are
compared with the predictions of a scaling theory.
