论文标题
在热状态下游离量子粒子的均方根位移
Mean square displacement of a free quantum particle in a thermal state
论文作者
论文摘要
均方根位移$ \ langle \ left（x（t）-x（0）\右）^2 \ 2 \ rangle $机械地评估了热平衡的质量$ m $的位置的$ x $。获得了一个分析表达式，该表达式显示了均方根位移随时间的初始二次增加，然后以线性生长为单位，其斜率$ \ hbar/m $，与经典统计力学的结果相当多。讨论了有关氦散射或自旋回波实验的可观察结果的讨论，以及它们可能根据基本自由粒子的均方位移的经典和量子机械表达来解释。
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.
