Brief History
This method is named after physicists Wentzel, Kramers, and Brillouin, who all developed it in 1926. In 1923, mathematician Harold Jeffreys had developed a general method of approximating solutions to linear, second-order differential equations, which includes the Schrödinger equation. Even though the Schrödinger equation was developed two years later, 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.
Earlier references to the method are: Carlini in 1817, Liouville in 1837, Green in 1837, Rayleigh in 1912 and 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.
The important contribution of Jeffreys, Wentzel, Kramers and Brillouin to the method was the inclusion of the treatment of turning points, connecting the evanescent and oscillatory solutions at either side of the turning point. For example, this may occur in the Schrödinger equation, due to a potential energy hill.
Read more about this topic: WKB Approximation
Famous quotes containing the word history:
“It’s not the sentiments of men which make history but their actions.”
—Norman Mailer (b. 1923)
“Let it suffice that in the light of these two facts, namely, that the mind is One, and that nature is its correlative, history is to be read and written.”
—Ralph Waldo Emerson (1803–1882)