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:
“For a transitory enchanted moment man must have held his breath in the presence of this continent, compelled into an aesthetic contemplation he neither understood nor desired, face to face for the last time in history with something commensurate to his capacity for wonder.”
—F. Scott Fitzgerald (1896–1940)
“The thing that struck me forcefully was the feeling of great age about the place. Standing on that old parade ground, which is now a cricket field, I could feel the dead generations crowding me. Here was the oldest settlement of freedmen in the Western world, no doubt. Men who had thrown off the bands of slavery by their own courage and ingenuity. The courage and daring of the Maroons strike like a purple beam across the history of Jamaica.”
—Zora Neale Hurston (1891–1960)