Klein paradox

This article needs attention from an expert in physics. The specific problem is: The diagrams and interpretation presented here need confirmation. WikiProject Physics may be able to help recruit an expert. (October 2019)

In 1929, physicist Oskar Klein^[1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However, Klein's result showed that if the potential is at least of the order of the electron mass, ${\displaystyle Ve\sim mc^{2}}$, the barrier is nearly transparent. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted.

The immediate application of the paradox was to Rutherford's proton–electron model for neutral particles within the nucleus, before the discovery of the neutron. The paradox presented a quantum mechanical objection to the notion of an electron confined within a nucleus.^[2] This clear and precise paradox suggested that an electron could not be confined within a nucleus by any potential well. The meaning of this paradox was intensely debated at the time.^[2]