不确定性关系：自1927年以来发现的一些引人注目的不等式小动物园
Uncertainty relations: a small zoo of remarkable inequalities discovered since 1927
AI总结：
本文综述了自1927年以来量子力学中不确定性关系的各种数学表述，包括传统海森堡不等式、施罗德inger和Robertson的修改、多非对易算符的推广，以及能量-时间不确定性关系的不同形式。
摘要：
本文简要回顾了自1927年以来量子力学中各种不确定性关系的数学表述。除了传统的海森堡不等式外，还考虑了施罗德inger和Robertson对它的修改，以及对多个非对易算符的推广。讨论了“熵”不等式和“局部”不确定性关系，以及连接波函数所谓总宽度和平均峰值宽度的不等式。还呈现了坐标和动量的高阶矩乘积的不等式。当量子态的“纯度”固定时，使不确定性关系更准确的不等式也得到了展示。还考虑了能量-时间不确定性关系的各种不同表述。
英文摘要：
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schrödinger and Robertson, as well as generalizations to sets of several noncommuting operators, are considered. The "entropic" inequalities and "local" uncertainty relations, together with inequalities which connect the so-called total width and the mean peak width of a wave function, are discussed. Inequalities for the products of higher order moments of the coordinate and momentum are presented. Inequalities making the uncertainty relations more accurate when the "purity" of a quantum state is fixed are demonstrated. Diverse formulations of the energy-time uncertainty relations are considered.
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