  The systematical studies on the dynamical approach of wavefunction collapse
in quantum measurement are reported in this paper based on the Hepp-Coleman's
model and its generalizations. Under certain physically reasonable conditions,
which are easily satisfied by the practical problems, it is shown that the
off-diagonal elements of the reduced density matrix vanish in quantum
mechanical evolution process in the macroscopic limit with a very large
particle number N. Various examples with detector made up of oscillators of
different spectrum distribution are used to illustrate this observations . With
the two-level system as an explicit illustration, the quantum information
entropy is exactly obtained to quantitatively describe the degree of
decoherence for the so-called partial coherence caused by detector. The entropy
for the case with many levels is computed based on perturbation method in the
limits with very large and very small N. As an application of this general
approach for quantum measurement, a dynamical realization of the quantum Zeno
effect are present to analyse its recent testing experiment in connection with
a description of transition in quantum information entropy. Finally, the Cini's
model for the correlation between the states of the measured system and the
detector is generalized for the case with many energy-level.
