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The Bohr–Sommerfeld model (also known as the Sommerfeld model or Bohr–Sommerfeld theory) was an extension of the Bohr model to allow elliptical orbits of electrons around an atomic nucleus. Bohr–Sommerfeld theory is named after Danish physicist Niels Bohr and German physicist Arnold Sommerfeld .
The category of quantum models encompasses a variety of exactly solvable problems in quantum mechanics. Each exactly solvable problem is of interest for several reasons. It provides a test case for methods applicable to other problems. It can be used as a starting point for perturbation theory.
When Bohr began his work on a new atomic theory in the summer of 1912 [8]: 237 the atomic model proposed by J J Thomson, now known as the Plum pudding model, was the best available. [9]: 37 Thomson proposed a model with electrons rotating in coplanar rings within an atomic-sized, positively-charged, spherical volume. Thomson showed that this ...
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
Precision tests of QED have been performed in low-energy atomic physics experiments, high-energy collider experiments, and condensed matter systems. The value of α is obtained in each of these experiments by fitting an experimental measurement to a theoretical expression (including higher-order radiative corrections) that includes α as a parameter.
This model exhibits confinement of the fermions and as such, is a toy model for QCD. A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as r {\displaystyle r} , instead of 1 / r {\displaystyle 1/r} in 4 dimensions, 3 spatial, 1 time.
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But for Bohr the important result was the use of classical analogies and the Bohr atomic model to fix inconsistencies in Planck's derivation of the blackbody radiation formula. [9]: 118 Bohr used the word "correspondence" in italics in lectures and writing before calling it a correspondence principle. He viewed this as a correspondence between ...