关于多样性即兴创作的一个主题：圆上的不确定性关系
On a subject of diverse improvisations: The uncertainty relations on a circle
摘要：
有争议的问题的不确定性关系（UR）的一个更一般的问题，这是指量子描述的角度观测值$L_z$和$ϕ$被视为一个特定的元素。发现即兴的$L_z-ϕ$ UR受到不可追溯缺陷的影响。同样与一个被广泛接受的信念相矛盾的是，量子力学的通常程序被证明是精确地适用于$L_z-ϕ$对。适用性涉及已知的圆形运动和不太为人所知的非圆形旋转运动。所提出的事实有助于作为论据得出以下不容置疑的结论：（i）必须否认对乌拉圭回合的传统解释是一种不正确的学说，（ii）对于$L_z-ϕ$对的自然物理考虑，来自通常量子力学的结果是足够的，而即兴的$L_z-ϕ$ UR必须作为无意义的公式而被拒绝，以及（iii）量子测量的描述必须在相对于通常的量子力学不同和附加的框架中进行。
英文摘要：
The disputed question of uncertainty relations (UR) on a circle is regarded as a particular element of a more general problem which refers to the quantum description of angular observables $L_z$ and $ϕ$. The improvised $L_z-ϕ$ UR are found to be affected by unsourmontable shortcomings. Also in contradiction with a largely accepted belief it is proved that the usual procedures of quantum mechanics are accurately applicable for the $L_z-ϕ$ pair. The applicability regards both the known circular motions and the less known non-circular rotational motions. The presented facts contribute as arguments to the following indubitable conclusions: (i) the traditional interpretation of UR must be denied as an incorrect doctrine, (ii) for a natural physical consideration of the the $L_z-ϕ$ pair the results from the usual quantum mechanics are sufficient while the improvised $L_z-ϕ$ UR must be rejected as senseless formulas and (iii) the descriptions of quantum measurements have to be done in a framework which is distinct and additional in respect with the usual quantum mechanics.
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