Boundary Value Problems in Electrodynamics and Quantum Mechanics: Palpable Parallels

In this article, we describe the analogy between some boundary value problems in electrodynamics and quantum mechanics, which evidently results due to the plane wave solutions of the associated wave equations and similar boundary conditions. As the first example, the reflection and transmission coefficients for normal incidence of plane electromagnetic waves on the interface of two dielectric media are compared with that for the one-dimensional step potential problem in quantum mechanics. In the second example, we take a problem from Griffiths’s electrodynamics and discuss the analogy with a quantum mechanical problem.