Eikonal approximation

The eikonal approximation is a method of approximation useful in wave scattering equations withing the realms of quantum mechanics, optics, quantum elctrodynamics, and partial wave expansion

Informal description

The main advantage the eikonal approximation others is that the equations reduce to a differential equation in a single variable. This reduction into a single variable is the result of the straight line approximation or the eikonal approximation which allows us to choose the straight line as a special direction.

==Relation to the WKB approximation The early steps involved in the eikonal approximation in quantum mechanics are very closely related to the WKB approximation. The WKB approximation involves an expansion in terms of Planck's constant. It, like the eikonal approximation, reduces the equations into a differential equation in a single variable. But the difficulty with the WKB approximation is that this variable is described by the trajectory of the particle which, in general, is complicated. The advantage of the eikonal approximation is that the classical trajectory is a straight line.

References

• [1]Eikonal Approximation K. V. Shajesh Department of Physics and Astronomy, University of Oklahoma