标题： 运动方程的哈密顿量量化 显示英文标题

标题： Quantization of the Hamilton Equations of Motion

摘要： 量子力学中的基本问题之一是找到正确的量子图像，以对应于实验测量的经典可观测量。 我们研究了适当的量子化规则，该规则将产生一个符合运动方程的量子模拟的哈密顿量，其中包括对算符相对于另一个算符的微分。 为了赋予这种微分的意义，玻恩和约丹建立了两种称为第一类和第二类微分商的定义。 在本文中，我们修改了第一类微分商的定义，并建立了其与对应于不同量子化的不同基算符的第二类微分商的一致性。 还研究了包括对算符的负幂次微分和多重微分在内的定理和微分规则。 我们证明了从魏尔、最简单对称和玻恩-约旦量子化得到的哈密顿量都满足量子运动方程所需的代数结构。 显示英文摘要

摘要： One of the fundamental problems in quantum mechanics is finding the correct quantum image of a classical observable that would correspond to experimental measurements. We investigate for the appropriate quantization rule that would yield a Hamiltonian that obeys the quantum analogue of Hamilton's equations of motion, which includes differentiation of operators with respect to another operator. To give meaning to this type of differentiation, Born and Jordan established two definitions called the differential quotients of first type and second type. In this paper we modify the definition for the differential quotient of first type and establish its consistency with the differential quotient of second type for different basis operators corresponding to different quantizations. Theorems and differentiation rules including differentiation of operators with negative powers and multiple differentiation were also investigated. We show that the Hamiltonian obtained from Weyl, simplest symmetric, and Born-Jordan quantization all satisfy the required algebra of the quantum equations of motion.