WKB approximation: Difference between revisions

Revision as of 16:17, 4 April 2025

Revision as of 11:38, 9 April 2025

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This method is named after physicists [[Gregor Wentzel]], [[Hendrik Anthony Kramers]], and [[Léon Brillouin]], who all developed it in 1926.<ref name=Wentzel-1926/><ref name=Kramers-1926/><ref name=Brillouin-1926/><ref>{{harvnb|Hall|2013}} Section 15.1 </ref> In 1923,<ref name=Jefferys-1924/> 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,<ref name=Carlini-1817/>, [[Joseph Liouville]] in 1837,<ref name=Liouville/>, [[George Green (mathematician)|George Green]] in 1837,<ref name=Green-1837/>, [[Lord Rayleigh]] in 1912<ref name=Rayleigh-1912/> and [[Richard Gans]] in 1915.<ref name=Gans-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

| title = Atmosphere-ocean dynamics

| author = Adrian E. Gill