Quantum trajectories and the Bohm time constant

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• 作者：Antonio B. Nassar ; ^{anassar@hw.com} ; ^{nassar@ucla.edu}
• 关键词：Bohmian trajectories ; Bohmian mechanics
• 刊名：Annals of Physics
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：331
• 期：Complete
• 页码：317-322
• 全文大小：356 K

文摘

This work proposes a new logarithmic nonlinear Schr?dinger equation to describe the dynamics of a wave packet under continuous measurement. Via the method of quantum trajectories formalism of the Bohmian model of quantum mechanics, it is shown that this continuous measurement alters the dynamical properties of the measured system. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge asymptotically in time to classical trajectories. So, continuous measurements not only disturb the particle but compel it to eventually converge to a Newtonian regime. The rate of convergence depends on what is defined here as the Bohm time constant which characterizes the resolution time of the measurement. If the initial wave packet width is taken to be equal to 2.8¡Á10^?15?m (the approximate size of an electron) then the Bohm time constant is found to be about 6.8¡Á10^?26?s.