In 1929 Oskar Klein stumbled into an apparent paradox when trying to describe the scattering of a relativistic electron by a square potential using Dirac's wave equation. … In order to capture the essence of the problem without entering into unnecessary complication we will study Klein's paradox in the context of the Klein– Gordon equation.
Ch. 1 : Why Do We Need Quantum Field Theory After All? - An Invitation to Quantum Field Theory (2012)