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(quantum mechanics) The paradox whereby, according to the Dirac electron theory, an electron can penetrate into a potential barrier which is greater than twice the rest energy of the electron (about 1 MeV) by making a transition from a positive energy state to a negative energy state, provided the potential change occurs over a distance on the order of a Compton wavelength or less.
Named after the Swedish physicist Oskar Klein, the Klein Paradox is a property of relativistic quantum mechanics pertaining to the scattering of a wave function from a potential barrier. When the incoming energy of a particle is less than the height of the barrier, the particle should classically be reflected with 100% certainty. But the Klein-Gordon or Dirac equations have a classically spurious transmitted wave into the potential region, where the electron should classically not be able to go by energy conservation. In a quantum context, i.e., non-classically, the transmitted wave function solution physically describes propagation of an anti-particle of the originally incident particle1. This physical interpretation agrees with experiment but precludes a single-particle interpretation of relativistic quantum mechanics. The resulting combination of quantum mechanics with special relativity without a single particle interpretation of a wave function at any given point leads to quantum field theory².
Although in a modern field theoretical interpretation of the Dirac equation the Klein paradox is automatically resolved, it continues to inspire publications today. In 2004, Piotr Krekora, Q. Charles Su, and Rainer Grobe at Illinois State University wrote: "The Klein paradox in spatial and temporal resolution" P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Using computer simulations they were able to show that the transmitted wave is the amount of suppression of pair creation at the barrier due to Pauli exclusion from the incoming electron. Except for a stream of positrons, there are no electrons under the barrier and the incoming electron is 100% reflected, although it gets entangled with the other electrons and positrons that are created at the barrier.
1Strange, Paul. 1998. Relativistic Quantum Mechanics. Cambridge U Press: Cambridge. 85,151-2.
²See such as: Weinberg, Steven. 1996 (volumes 1 & 2), 2000 (vol. 3). The Quantum Theory of Fields. Cambridge U Press: Cambridge.
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