Zero-range potential for the Dirac equation in two and three space dimensions: Elementary proof of Svendsen’s theorem

There is a theorem proved by Svendsen which implies that a zero-range (δ-function) potential cannot be defined for the Dirac equation in two and three space dimensions. We give an elementary proof of the theorem by examining the solution of the Dirac equation with a square-well potential of finite range and taking the zero-range limit.