  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 view in teaching this
important quantum field theory model using basic electrostatics.
