The rigorous mathematical theory of this approximation for linear second-order differential equations was developed by Harold Jeffreys.
In quantum field theory, it is equivalent to one-loop Feynman diagrams. The idea is originally attributed to Lord Rayleigh, who used it to analyze the propagation of an optical disturbance in a nonuniform medium. In his version, he assumed that the wave number was proportional to the index of refraction. The rigorous mathematical theory of this approximation for linear second-order differential equations was developed by Harold Jeffreys. For 10 points, name this approximation valid when the potential varies slowly compared to the wave function, a truncated asymptotic series named after three physicists.
In quantum field theory, it is equivalent to one-loop Feynman diagrams.
{W}entzel-{K}ramers-{B}rillouin-Jeffreys approximation [accept any permutation of the names or letters that contains the required/underlined information]