Jump to content

Plane-wave expansion

From Wikipedia, the free encyclopedia
(Redirected from Plane wave expansion)

In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves: where

In the special case where k is aligned with the z axis, where θ is the spherical polar angle of r.

Expansion in spherical harmonics

[edit]

With the spherical-harmonic addition theorem the equation can be rewritten as where

Note that the complex conjugation can be interchanged between the two spherical harmonics due to symmetry.

Applications

[edit]

The plane wave expansion is applied in

See also

[edit]

References

[edit]
  • Digital Library of Mathematical Functions, Equation 10.60.7, National Institute of Standards and Technology
  • Rami Mehrem (2009), The Plane Wave Expansion, Infinite Integrals and Identities Involving Spherical Bessel Functions, arXiv:0909.0494, Bibcode:2009arXiv0909.0494M