WKB approximation: Difference between revisions

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== Brief history ==
This method is named after physicists [[Gregor Wentzel]], [[Hendrik Anthony Kramers]], and [[Léon Brillouin]], who all developed it in 1926.<ref>{{cite book |first=Brian C. harvnb|last=Hall |chapter=The WKB Approximation |title=Quantum Theory for Mathematicians |___location= |publisher=Springer |year=2013}} |pages=305–331Section |doi=1015.1007/978-1-4614-7116-5_15 |isbn=978-1-4614-7115-8 }}</ref> In 1923, mathematician [[Harold Jeffreys]] had developed a general method of approximating solutions to linear, second-order differential equations, a class that includes the [[Schrödinger equation]]. The Schrödinger equation itself was not developed until two years later, and Wentzel, Kramers, and Brillouin were apparently unaware of this earlier work, so Jeffreys is often neglected credit. Early texts in quantum mechanics contain any number of combinations of their initials, including WBK, BWK, WKBJ, JWKB and BWKJ. An authoritative discussion and critical survey has been given by Robert B. Dingle.<ref>{{cite book |first=Robert Balson |last=Dingle |title=Asymptotic Expansions: Their Derivation and Interpretation |publisher=Academic Press |year=1973 |isbn=0-12-216550-0 }}</ref>
 
Earlier appearances of essentially equivalent methods are: [[Francesco Carlini]] in 1817, [[Joseph Liouville]] in 1837, [[George Green (mathematician)|George Green]] in 1837, [[Lord Rayleigh]] in 1912 and [[Richard Gans]] in 1915. Liouville and Green may be said to have founded the method in 1837, and it is also commonly referred to as the Liouville–Green or LG method.<ref>{{cite book