Editing Old quantum theory (section)

== Limitations ==
The old quantum theory had some limitations:<ref>{{cite book |first=G.S. |last=Chaddha |title=Quantum Mechanics |publisher=New Age international |location=New Delhi |year=2006 |isbn=978-81-224-1465-3 |pages=8–9 |url=https://books.google.com/books?id=Bzj2JcPeAHAC&pg=PA9}}</ref>
* The old quantum theory provides no means to calculate the intensities of the spectral lines.
* It fails to explain the anomalous Zeeman effect (that is, where the spin of the electron cannot be neglected).
* It cannot quantize "chaotic" systems, i.e. dynamical systems in which trajectories are neither closed nor periodic and whose analytical form does not exist. This presents a problem for systems as simple as a 2-electron atom which is classically chaotic analogously to the famous gravitational [[three-body problem]].
However it can be used to describe atoms with more than one electron (e.g. Helium) and the Zeeman effect.<ref>{{cite journal|last1=Solov'ev|title=Classical approach in atomic physics|journal= European Physical Journal D|year=2011|volume=65|pages=331–351|doi=10.1140/epjd/e2011-20261-6|arxiv = 1003.4387 |bibcode = 2011EPJD...65..331S|first1=E. A.|issue=3 |s2cid=119204790}}</ref> 
It was later proposed that the old quantum theory is in fact the [[WKB approximation|semi-classical approximation]] to the canonical quantum mechanics<ref>
{{cite book
 |author=[[Lev Landau|L.D. Landau]], [[Evgeny Lifshitz|E.M. Lifshitz]]
 |year=1977
 |title=Quantum Mechanics: Non-Relativistic Theory
 |edition=3rd |volume=3
 |publisher=[[Pergamon Press]]
 |isbn=978-0-08-020940-1
}}</ref> but its limitations are still under investigation.