Electrostatic simulation of the Jackiw-Rebbi zero energy state

We present an analogy between the one dimensional Poisson equation in inhomogeneous media and the Dirac equation in one space dimension with a Lorentz scalar potential for zero energy. We illustrate how the zero energy state in the Jackiw-Rebbi model can be implemented in a simple one dimensional electrostatic setting by using an inhomogeneous electric permittivity and an infinite charged sheet. Our approach provides a novel insight into the Jackiw-Rebbi zero energy state and provides a helpful way to visualize and teach this important quantum field theory model using basic electrostatics.