Electronic Maxwell’s equations

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.