热态下自由量子粒子的均方位移
Mean square displacement of a free quantum particle in a thermal state
摘要：
在热平衡下，质量为$m$的自由粒子的位置$x$的均方位移$\langle\left(x(t)-x(0)\right)^2\rangle$被量子力学地评估。得到了一个解析表达式，它表明均方位移随时间呈二次增长，然后呈线性增长，其斜率为$\hbar/m$，与经典统计力学的结果有很大差异。结果进行了讨论，从氦散射或自旋回波实验的观测值，其可能的解释方面的经典和量子力学的表达基本上是自由的粒子的均方位移。
英文摘要：
The mean square displacement $\langle\left(x(t)-x(0)\right)^2\rangle$ of the position $x$ of a free particle of mass $m$ at thermal equilibrium is evaluated quantum mechanically. An analytical expression is obtained which shows an initial quadratic increase of the mean square displacement with time and later on a linear growth, with the slope $\hbar/m$, quite at variance with the result from classical statistical mechanics. Results are discussed in relation to observables from helium scattering or spin-echo experiments, and their possible interpretation in terms of the classical and quantum mechanical expression for the mean square displacement of an essentially free particle.
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