论文标题
圆上的不确定性关系和最小波数据包
Uncertainty Relation and Minimum Wave Packet on Circle
论文作者
论文摘要
我们讨论了封闭的一维系统（圆圈）的不确定性关系（UR）。在这样的系统中，我们不能将沿圆的角度用作位置变量。否则，我们就平均位置和标准偏差（SD）的定义以及角动量的Hermitian特性遇到困难。从这些原因中，我们将位置变量定义为具有倾斜$ ϕ $的定期属性的笛卡尔变量$（x，y）$。以相同的方式，我们通过使用该变量来定义SD。然后我们获得了两个UR。我们还讨论了圆圈上的最小波数据包（MWP）。 MWP由Von Mises分布函数表达。接下来，我们通过将两个UR组合为$ x $和$ y $来构建总UR。此外，我们将变量扩展到$（x_n，y_n）$ \; $ n = 1,2,3，\ cdots $，我们有一系列无限的URS。我们考虑了这种扩展的URS的含义。
We discuss on the uncertainty relation (UR) for a closed one dimensional system (circle). In such a system, we cannot use the angle along the circle as a position variable. Otherwise we meet difficulties about the definition of the average position and the standard deviation (SD), and Hermitian property of angular momentum. From these reasons, we define the position variable as Cartesian variable $(X,Y)$ that have the periodic property for angle $ϕ$. In the same way we define a SD by using that variables. Then we obtain two URs. We also discuss the minimum wave packet (MWP) on the circle. MWPs are expressed by von Mises distribution functions. Next we construct total URs by combining two URs for $X$ and $Y$. Furthermore, we extend the variables to $(X_n, Y_n)$ \; with $n= 1,2,3,\cdots$ and we have infinite series of total URs. We consider the meaning of such extended URs.
