To date, the wave nature of electron has been widely researched, together with its similarity to optics. To unify electronic waves and electromagnetic waves, we establish four equations analogous to Maxwell’s equations by expressing the Dirac equation in terms of the quaternions. We develop some fundamental theories from the electronic version of Maxwell’s equations. In practice, solving electron wave problem is convenient without appearance of quantum operators such as Pauli matrices. The benefit is its potential in the analysis and applications of diverse electron beams, for example, phase-shift control. Moreover, physical quantities represented by electronic vector fields are notably similar to those in optics, making it possible to apply some ideas developed in optics in the research of electron.

迄今为止，已经广泛研究了电子的波特性及其与光学的相似性。为了统一电子波和电磁波，我们通过用四元数表示狄拉克方程，建立了类似于麦克斯韦方程的四个方程。我们从电子形式的麦克斯韦方程组开发了一些基础理论。实际上，解决电子波问题很方便，而不会出现诸如Pauli矩阵之类的量子算符。好处在于它在各种电子束的分析和应用中的潜力，例如相移控制。而且，由电子矢量场表示的物理量与光学中的物理量显着相似，这使得可以将光学中发展的一些思想应用到电子研究中。