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A new quantum mechanical description of the dynamics of wave packet undercontinuous measurement is formulated via Bohmian mechanics. The solution tothis equation is found through a wave packet approach which establishes adirect correlation between a classical variable with a quantum variabledescribing 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 thanapproaches using restrited path integrals and master equation approaches. Thiswork shows how the extremely irregular character of classical chaos can bereconciled with the smooth and wavelike nature of phenomena on the atomicscale. It is demonstrated that a wave packet under continuous quantummeasurement displays both chaotic and non-chaotic features. The Lyapunovcharacteristic exponents for the trajectories of classical particle and thequantum wave packet center of mass are calculated and their chaoticities aredemonstrated to be about the same. Nonetheless, the width of the wave packetexhibits a non-chaotic behavior and allows for the possibility to beat thestandard quantum limit by means of transient, contractive states.

Wave Packet under Continuous Measurement via Bohmian Mechanics