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, , 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]
^Klein, O. (1929). "Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac". Zeitschrift für Physik. 53 (3–4): 157–165. Bibcode:1929ZPhy...53..157K. doi:10.1007/BF01339716. S2CID 121771000.
^ abStuewer, Roger H. (1985). "Niels Bohr and Nuclear Physics". In French, A. P.; Kennedy, P. J. (eds.). Niels Bohr: A Centenary Volume. Harvard University Press. pp. 197–220. ISBN 0674624165.
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list...
Oskar Benjamin Klein (Swedish: [ˈklajn]; 15 September 1894 – 5 February 1977) was a Swedish theoretical physicist. Oskar Klein is known for his work on...
The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally...
correctly identify what is observable in this theory. Much of the apparently paradoxical behavior implied by the Dirac equation amounts to a misidentification...
Klein, P. (1981). Certainty: a Refutation of Scepticism, Minneapolis, MN: University of Minnesota Press. Kroedel, T. (2012). "The Lottery Paradox, Epistemic...
Heisenberg uncertainty relation of quantum mechanics. The Kleinparadox, discovered by Oskar Klein in 1928, presented further quantum mechanical objections...
In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed...
The buttered cat paradox is a common joke based on the combination of two adages: Cats always land on their feet. Buttered toast always lands buttered...
determine the statistics of the nucleus.": 117–118 The Kleinparadox, discovered by Oskar Klein in 1928, presented further quantum mechanical objections...
coefficients that are not bounded. This phenomenon is known as the Kleinparadox. The apparent paradox disappears in the context of quantum field theory. The Heaviside...
no gap between the positive and negative energy spectra, as in the Kleinparadox. More accurate calculations taking into account the effects of the finite...
indeed too good to be true. Fisher's analysis gave rise to the Mendelian paradox: Mendel's reported data are, statistically speaking, too good to be true...
Together with Alex Hansen he provided the natural explanation of the Kleinparadox by including the effects of antiparticles from the Dirac equation In...
Hamiltonian's spectrum. 1929: Oskar Klein discovers the Kleinparadox Oskar Klein and Yoshio Nishina derive the Klein–Nishina cross section for high energy...
of molecular orbital 1929 Oskar Klein discovers the Kleinparadox 1929 Oskar Klein and Yoshio Nishina derive the Klein–Nishina cross section for high energy...
19th century. Terminal lucidity is a narrower term than the phenomenon paradoxical lucidity where return of mental clarity can occur anytime (not just before...
Schrödinger equation does not apply to massless particles; instead the Klein–Gordon equation is required. The mechanical model giving rise to the negative...
the Van de Graaff generator. Oskar Klein discovers the Kleinparadox. Oskar Klein and Y. Nishina derive the Klein–Nishina cross section for high energy...
Socrates challenges Meno's argument, often called "Meno's Paradox" or the "Learner's Paradox", by introducing the theory of knowledge as recollection (anamnesis)...
Spacetimes", Physical Review D 35 (1987) 3783-3795. Corinne A. Manogue, "The KleinParadox and Superradiance", Annals of Physics 181 (1988) 261-283. "Paradigms...
The sad clown paradox is the contradictory association, in performers, between comedy and mental disorders such as depression and anxiety. For those affected...