WKB approximation
- Category
- STANDARD MATHEMATICS
- Definition
- An asymptotic method for differential equations with wave-like solutions, typically valid away from turning points.
- Math Level
- SPECIALIST
- Index Excerpt
- WKB; Wentzel–Kramers–Brillouin
The WKB approximation is an asymptotic method for differential equations with a large or slowly varying parameter, especially equations with wave-like solutions.
Away from turning points, WKB-type formulas often describe oscillation and exponential behaviour effectively. Near a turning point the usual approximation breaks down and is commonly replaced by a uniform Airy-type description.
See also: asymptotic, turning point, Airy function, scaling law.