标题： 线性与非线性量子力学系统中的可测性 显示英文标题

标题： Measurability in Linear and Non-Linear Quantum Mechanical Systems

摘要： 通过连续测量，研究了在某一时刻可观测量$\A(t_0)$和时间平均可观测量$\bar \A=1/T\int \A(t')dt'$的可测量性，适用于线性和特别是非线性量子力学系统。 我们认为只有当精确（非微扰）解已知时，才可能进行精确测量。 显示在非线性情况下，对于精度为$\Delta \bar \A < \Delta \bar \A_{min}(T)$的测量，微扰方法会失败，从而导致精度的限制。 因此，为了通过连续测量准备非线性系统的初始纯态，必须知道精确的非微扰解。 显示英文摘要

摘要： The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for non-linear quantum mechanical systems. We argue that only when the exact (non-perturbative) solution is known, an exact measurement may be possible. A perturbative approach is shown to fail in the non-linear case for measurements with accuracy $\Delta \bar \A < \Delta \bar \A_{min}(T)$, giving rise to a restriction on the accuracy. Thus, in order to prepare an initial pure state of a non-linear system, by means of a continuous measurement, the exact non-perturbative solution must be known.