Editing Old quantum theory (section)

{{Short description|Predecessor to modern quantum mechanics (1900–1925)}}
{{Quantum mechanics|cTopic=Background}}

The '''old quantum theory''' is a collection of results from the years 1900–1925,<ref>{{cite book |title=Subtle is the Lord: The Science and the Life of Albert Einstein |edition=illustrated |first1=Abraham |last1=Pais |publisher=OUP Oxford |year=2005 |isbn=978-0-19-280672-7 |page=28 |url=https://books.google.com/books?id=0QYTDAAAQBAJ}} [https://books.google.com/books?id=0QYTDAAAQBAJ&pg=PA28 Extract of page 28]</ref> which predate modern [[quantum mechanics]]. The theory was never complete or self-consistent, but was instead a set of [[heuristic]] corrections to [[classical mechanics]].<ref>{{cite book|last = ter Haar|first =D.|title =The Old Quantum Theory|url = https://archive.org/details/oldquantumtheory0000haar|url-access = registration|publisher=Pergamon Press|year=1967|pages = [https://archive.org/details/oldquantumtheory0000haar/page/206 206]|isbn = 978-0-08-012101-7}}</ref> The theory has come to be understood as the [[WKB approximation#Application to the Schr.C3.B6dinger equation|semi-classical approximation]]<ref>Semi-classical approximation. ''Encyclopedia of Mathematics''. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-classical_approximation</ref> to modern quantum mechanics.<ref>{{cite book|last=Sakurai, Napolitano|title=Modern Quantum Mechanics|publisher=Pearson|year=2014|isbn=978-1-292-02410-3|chapter=Quantum Dynamics}}</ref> The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by [[Edmund Stoner]] and the [[Pauli exclusion principle]], both of which were premised on [[Arnold Sommerfeld]]'s enhancements to the [[Bohr model]] of the atom.<ref>{{cite journal | doi=10.2307/27757389 | jstor=27757389 | last1=Kragh | first1=Helge | title=Niels Bohr's Second Atomic Theory | journal=Historical Studies in the Physical Sciences | year=1979 | volume=10 | pages=123–186 }}</ref><ref>Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.7.</ref>

The main tool of the old quantum theory was the Bohr–Sommerfeld quantization condition, a procedure for selection of certain allowed states of a classical system: the system can then only exist in one of the allowed states and not in any other state.