  A new quantum mechanical description of the dynamics of wave packet under
continuous measurement is formulated via Bohmian mechanics. The solution to
this equation is found through a wave packet approach which establishes a
direct correlation between a classical variable with a quantum variable
describing the dynamics of the center of mass and the width of the wave packet.
The approach presented in this paper gives a comparatively clearer picture than
approaches using restrited path integrals and master equation approaches. This
work shows how the extremely irregular character of classical chaos can be
reconciled with the smooth and wavelike nature of phenomena on the atomic
scale. It is demonstrated that a wave packet under continuous quantum
measurement displays both chaotic and non-chaotic features. The Lyapunov
characteristic exponents for the trajectories of classical particle and the
quantum wave packet center of mass are calculated and their chaoticities are
demonstrated to be about the same. Nonetheless, the width of the wave packet
exhibits a non-chaotic behavior and allows for the possibility to beat the
standard quantum limit by means of transient, contractive states.
