We present a succinct way to quantize Maxwell's equations. We begin by discussing the random nature of quantum observables. Then we present the quantum Maxwell's equations and give their physical meanings. Due to the mathematical homomorphism between the classical and quantum cases [1], the derivation of quantum Maxwell's equations can be simplified. First, one needs only to verify that the classical equations of motion are derivable from a Hamiltonian by energy-conservation arguments. Then the quantum equations of motion follow due to homomorphism, which applies to sum-separable Hamiltonians. Hence, we first show the derivation of classical Maxwell's equations using Hamiltonian theory. Then the derivation of the quantum Maxwell's equations follows in an analogous fashion. Finally, we apply this quantization procedure to the dispersive medium case. (This article is written for the classical electromagnetic community assuming little knowledge of quantum theory, an introduction of which can be found in [2, Lecs. 38 and 39].)

中文翻译：

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量子麦克斯韦方程变得简单：采用标量和矢量势公式


我们提出了一种量化麦克斯韦方程组的简洁方法。我们首先讨论量子可观测量的随机性质。然后我们提出了量子麦克斯韦方程组并给出了它们的物理意义。由于经典情况和量子情况之间的数学同态性[1]，量子麦克斯韦方程组的推导可以得到简化。首先，我们只需要验证经典运动方程可以通过能量守恒论证从哈密顿量导出。然后，由于同态，量子运动方程成立，这适用于和可分的哈密顿量。因此，我们首先展示使用哈密顿理论对经典麦克斯韦方程组的推导。然后以类似的方式推导量子麦克斯韦方程组。最后，我们将此量化过程应用于色散介质情况。 （本文是为经典电磁界编写的，假设对量子理论知之甚少，其介绍可以在 [2，Lecs. 38 和 39] 中找到。）