Klein paradox

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Named after the Swedish scientist Oskar Klein, the Klein Paradox occurs in relativistic quantum mechanics if an electron is shot into a repulsive electrostatic barrier. As the incoming energy of the electron is less than that of the barrier, the electron should be reflected with 100% certainty. The numerical solution to the Dirac equation (in its single-particle interpretation) predicts a spurious transmitted portion of the wave function solution inside the barrier, where according to classical arguments the electron is forbidden to be. It was not clear how to interprete this unusual transmitted portion of the wave function.

The 75-year-old paradox was finally resolved in 2004 by Piotr Krekora, Q. Charles Su, and Rainer Grobe at Illinois State University. See their publication: "The Klein paradox in spatial and temporal resolution" P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004). Using computer simulations to quantum field theory they were able to show that the transmitted wave function portion is the amount of suppression of (spontaneously induced) electron-positron pair creation at the barrier due to Pauli blocking by the incoming electron. Except the stream of positrons, there are no real electrons under the barrier and the incoming electron is 100% reflected while getting entangled with the other electrons and positrons that are created at the barrier.