Klein Paradox

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 ertainty. 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.
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This is the name sometimes given to the logic that shows there can be no electrons in the nucleus of an atom (hence a beta particle is created at the instant of radioactive emission). The 'size' of an electron is associated with its de Broglie wavelength; roughly speaking this matter wavelength for a bound electron in an atomic orbit is of the order of the circumference of the orbit. The greater the energy the shorter the wavelength (E=hc/lambda). Thus for an electron to have a wavelength small enough to be inside the nucleus of an atom (which has a diameter ~10000 times less than the whole atom) its energy must be so great that forces would have to be unacceptably large to bind it.