柯西-施瓦兹不等式与不确定度关系

Cauchy-Schwartz Inequality and the Uncertainty Relation

从自然界不同空间最基本的不等量关系出发,导出了著名的柯西-施瓦兹不等式。将其应用于微观世界量子系统,并考虑到希尔伯特空间状态物理量算符的线性厄米性质,进一步推演得到量子力学的基本规律——不确定度关系。讨论了不确定度关系的重大意义,它是微观粒子波粒二象性的客观反映,是保持原子乃至整个世界稳定的基础。

The famous Cauchy-Schwarz inequality is deduced from the fundamental unequal relationship in different spaces in the nature.Considering the linear Hermitian property of the state physical operators on the Hilbert space,the uncertainty relation is derived by applying the inequality to the quantum system of microcosm.The significance of the uncertainty relation which is the objective report of the wave-particle duality of the microscopic particle and the basis for keeping the stability of atoms and even the whole world is discussed.