Editing Old quantum theory (section)

== History ==

The old quantum theory was instigated by the 1900 work of [[Max Planck]] on the emission and absorption of light in a [[black body]] with his discovery of [[Planck's law]] introducing his [[Planck constant|quantum of action]], and began in earnest after the work of [[Albert Einstein]] on the [[Einstein solid|specific heats]] of solids in 1907 brought him to the attention of [[Walther Nernst]].<ref>Thomas Kuhn, Black-Body Theory and the Quantum Discontinuity, 1894–1912 (Chicago: University of Chicago Press, 1978)</ref> Einstein, followed by [[Peter Debye|Debye]], applied quantum principles to the motion of atoms, explaining the [[Schottky anomaly|specific heat anomaly]].

In 1910, [[Arthur Erich Haas]] further developed J. J. Thomson's atomic model in a paper<ref>
* Haas, Arthur Erich (1910) "Über die elektrodynamische Bedeutung des Planck'schen Strahlungsgesetzes und über eine neue Bestimmung des elektrischen Elementarquantums und der Dimension des Wasserstoffatoms". ''Sitzungsberichte der kaiserlichen Akademie der Wissenschaften in Wien''. Abt 2A, (119) pp 119-144.
* Haas A.E. ''Die Entwicklungsgeschichte des Satzes von der Erhaltung der Kraft''. Habilitation Thesis, Vienna, 1909.
* Hermann, A. ''Arthur Erich Haas, Der erste Quantenansatz für das Atom''. Stuttgart, 1965 [contains a reprint].
</ref> that outlined a treatment of the hydrogen atom involving quantization of electronic orbitals, thus anticipating the Bohr model (1913) by three years.

[[John William Nicholson]] is noted as the first to create an atomic model that quantized angular momentum as <math>h/(2\pi)</math>.<ref>
* {{cite journal |doi=10.1093/mnras/72.1.49|title=The Spectrum of Nebulium |year=1911 |last1=Nicholson |first1=J. W. |journal=Monthly Notices of the Royal Astronomical Society |volume=72 |pages=49–64 |doi-access=free |bibcode=1911MNRAS..72...49N }}
* {{cite journal |doi=10.1093/mnras/72.2.139|title=The Constitution of the Solar Corona. I.: Protofluorine |year=1911 |last1=Nicholson |first1=J. W. |journal=Monthly Notices of the Royal Astronomical Society |volume=72 |issue=2 |pages=139–150 |doi-access=free |bibcode=1911MNRAS..72..139N }}
* {{cite journal |doi=10.1093/mnras/72.8.677|title=The Constitution of the Solar Corona. IL |year=1912 |last1=Nicholson |first1=J. W. |journal=Monthly Notices of the Royal Astronomical Society |volume=72 |issue=8 |pages=677–693 |doi-access=free }}
* {{cite journal |doi=10.1093/mnras/72.8.693|title=On the New Nebular Line at 4353 |year=1912 |last1=Nicholson |first1=J. W. |journal=Monthly Notices of the Royal Astronomical Society |volume=72 |issue=8 |page=693 |doi-access=free |bibcode=1912MNRAS..72..693N }}
* {{cite journal |doi=10.1093/mnras/72.9.729|title=The Constitution of the Solar Corona. III |year=1912 |last1=Nicholson |first1=J. W. |journal=Monthly Notices of the Royal Astronomical Society |volume=72 |issue=9 |pages=729–740 |doi-access=free }}
</ref><ref>{{cite journal | jstor=41133258 | title=The Atomic Theory of John William Nicholson | last1=McCormmach | first1=Russell | journal=Archive for History of Exact Sciences | year=1966 | volume=3 | issue=2 | pages=160–184 | doi=10.1007/BF00357268 | s2cid=120797894 }}</ref> [[Niels Bohr]] quoted him in his 1913 paper of the Bohr model of the atom.<ref>{{cite journal | doi=10.1080/14786441308634955 | title=On the constitution of atoms and molecules | year=1913 | last1=Bohr | first1=N. | journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |series=Series 6 | volume=26 | issue=151 | pages=1–25 | bibcode=1913PMag...26....1B | url=https://zenodo.org/record/2493915 }}</ref>

In 1913, [[Niels Bohr]] displayed rudiments of the later defined [[correspondence principle]] and used it to formulate a [[Bohr Model|model]] of the [[hydrogen atom]] which explained the [[Atomic emission spectrum|line spectrum]].  In the next few years [[Arnold Sommerfeld]] extended the quantum rule to arbitrary integrable systems making use of the principle of [[adiabatic invariant|adiabatic invariance]] of the quantum numbers introduced by Lorentz and Einstein.  Sommerfeld made a crucial contribution<ref name="Sommerfeld">{{cite book |last=Sommerfeld |first=Arnold |title=Atombau und Spektrallinien' |publisher=Friedrich Vieweg und Sohn |year=1919 |isbn= |location=Braunschweig}}</ref> by quantizing the z-component of the [[angular momentum]], which in the old quantum era was called "space quantization" (German: ''Richtungsquantelung''). This model, which became known as the [[Bohr–Sommerfeld model]], allowed the orbits of the electron to be ellipses instead of circles, and introduced the concept of [[quantum degeneracy]]. The theory would have correctly explained the [[Zeeman effect]], except for the issue of electron [[Spin (physics)|spin]].  Sommerfeld's model was much closer to the modern quantum mechanical picture than Bohr's.

Throughout the 1910s and well into the 1920s, many problems were attacked using the old quantum theory with mixed results. Molecular rotation and vibration spectra were understood and the electron's spin was discovered, leading to the confusion of half-integer quantum numbers.  Max Planck introduced the [[zero point energy]] and Arnold Sommerfeld semiclassically quantized the relativistic hydrogen atom. [[Hendrik Kramers]] explained the [[Stark effect]]. [[Satyendra Nath Bose|Bose]] and Einstein gave the correct quantum statistics for photons.

[[Image: Drawing_of_Sommerfeld_atom.svg |thumb|310px|The Sommerfeld extensions of the 1913 solar system Bohr
model of the [[hydrogen atom]] showing the addition of elliptical orbits to explain spectral fine structure. The circular n=3 corresponds to a higher energy orbital.<ref>{{Cite web |title=Introduction to the Bohr Model |url=https://www.dumdummotijheelcollege.ac.in/pdf/1586768332.pdf |url-status=live |archive-url=https://web.archive.org/web/20240822100037/https://www.dumdummotijheelcollege.ac.in/pdf/1586768332.pdf |archive-date=2024-08-22 |website=Dum Dum Motijheel College}}</ref> n=3 has multiple orbits because of azimuthal quantum number.]]

Kramers gave a prescription for calculating transition probabilities between quantum states in terms of Fourier components of the motion, ideas which were extended in collaboration with [[Werner Heisenberg]] to a semiclassical matrix-like description of atomic transition probabilities. Heisenberg went on to reformulate all of quantum theory in terms of a version of these transition matrices, creating [[matrix mechanics]].

In 1924, [[Louis de Broglie]] introduced the wave theory of matter, which was extended to a semiclassical equation for matter waves by Albert Einstein a short time later. In 1926 [[Erwin Schrödinger]] found a completely quantum mechanical wave-equation, which reproduced all the successes of the old quantum theory without ambiguities and inconsistencies. Schrödinger's wave mechanics developed separately from matrix mechanics until Schrödinger and others proved that the two methods predicted the same experimental consequences. Paul Dirac later proved in 1926 that both methods can be obtained from a more general method called [[Transformation theory (quantum mechanics)|transformation theory]].

In the 1950s [[Joseph Keller]] updated Bohr–Sommerfeld quantization using Einstein's interpretation  of 1917,<ref>The Collected Papers of Albert Einstein, vol. 6, A. Engel, trans., Princeton U. Press,
Princeton, NJ (1997), p. 434</ref> now known as [[Einstein–Brillouin–Keller method]]. In 1971, [[Martin Gutzwiller]] took into account that this method only works for integrable systems and derived a [[Quantum chaos|semiclassical way of quantizing chaotic systems]] from [[path integral formulation|path integrals]].<ref>{{cite journal|title=Einstein's unknown insight and the problem of quantizing chaos|author=Stone, A.D.|journal=Physics Today|date=August 2005|volume=58|number=8|pages=37–43|url=https://www.eng.yale.edu/stonegroup/publications/phys_today.pdf|doi=10.1063/1.2062917|bibcode = 2005PhT....58h..37S }}</ref>