The Klein paradox is a counterintuitive prediction from relativistic quantum mechanics that describes how particles, such as electrons, behave when they encounter extremely steep or high potential barriers. It was first proposed by Oskar Klein in 1929 while analyzing the Dirac equation.
According to classical expectations, a particle hitting a barrier higher than its total energy should be reflected. However, the Klein paradox reveals that when the potential barrier becomes steep enough—comparable to or greater than twice the particle’s rest energy—relativistic particles can pass through the barrier with unexpectedly high probability, even approaching full transmission. In some cases, instead of being reflected, the particle appears to transform into its antiparticle and continue propagating.
This phenomenon arises because, at such high potentials, the barrier region allows the creation of particle-antiparticle pairs, enabling the particle to tunnel through by converting into its antiparticle. The paradox highlights the deep and non-intuitive consequences of combining quantum mechanics with special relativity, and it has modern analogues in systems like graphene, where charge carriers behave like massless Dirac particles and exhibit similar effects.