 in mathematical physics, the wkb approximation or wkb method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients. it is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing. the name is an initialism for wentzelâkramersâbrillouin. it is also known as the lg or liouvilleâgreen method. other often-used letter combinations include jwkb and wkbj, where the "j" stands for jeffreys. == 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 schrÃ¶dinger equation. even though the schrÃ¶dinger 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 liouvilleâgreen 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 schrÃ¶dinger equation, due to a potential energy hill. ==wkb metho
Approximations Asymptotic_analysis Mathematical_physics Theoretical_physics