In physics, the plane wave expansion expresses a plane wave as a sum of spherical waves,
Contents
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
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
The plane wave expansion is applied in
References
Plane wave expansion Wikipedia(Text) CC BY-SA