WKBmeetodites

WKBmeetodites is a term used in mathematical physics to denote a family of asymptotic approximation techniques derived from the Wentzel–Kramers–Brillouin (WKB) method for solving linear wave equations in the high-frequency or short-wavelength limit. The name blends the WKB acronym with a plural suffix to indicate a class of related methods. The central idea is to seek solutions in an exponential form with a phase divided by a small parameter, and to develop a series expansion for the phase and the amplitude.

In the standard approach, the leading order yields an eikonal equation for the phase, while subsequent orders produce transport equations for the amplitude and higher-correction terms. WKBmeetodites extend this framework to multi-dimensional, matrix-valued, or coupled systems, and to more sophisticated turning-point and Stokes-phenomenon treatments through uniform approximations and related constructions such as Maslov theory. They also emphasize phase-space perspectives and can incorporate ideas from Gaussian-beam and ray-based methods.

Applications of WKBmeetodites span several fields, including geometrical optics, quantum mechanics in the semiclassical regime, acoustics, and seismology. The methods are chosen to balance accuracy and computational efficiency, with variants differing in how turning points are handled, how error estimates are formulated, and how higher-order corrections are implemented. The concept is used to compare and systematize different WKB-type approximations, and to provide practical guidelines for selecting appropriate uniform or leading-order schemes in complex wave problems.