Abstract

The advanced technology of electron microscope has recently achieved Dennis Gabor's original concept of holographic reconstruction of electron microscope images.¹ This is due to the improved coherence property of electron waves and optical holography. This stimulated me to reexamine the analogy of electron waves and electromagnetic waves and clarify its physical meaning. First, the characteristic wave impedance of electron wave η_e is defined by the ratio of the Schrodinger wave function ψ and then the associated momentum state function ϕ: ${\eta }_e=\sqrt{E/2m}$, where E is the energy of electron and m is the mass or effective mass of an electron in either free space or solid-state materials. Note that the phase constant $\beta =\sqrt{2ME}/\hslash$ and the refractive index is defined by the ratio β. Second, using the boundary conditions consisting of continuity of both ψ and ϕ, we obtain the reflection and transmission coefficients for the obliquely incident electron wave. These coefficients correspond to those of the s wave of TE waves in electromagnetic optics. Total internal reflection exists, but the Brewster angle is missing in electron optics. The coherence theory of electron waves such as the Van Cittert-Zernike theorem and the intensity correlation are also discussed.