Plane-wave_expansion
Plane-wave expansion
Expressing a plane wave as a combination of spherical waves
In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves:
where
- i is the imaginary unit,
- k is a wave vector of length k,
- r is a position vector of length r,
- jℓ are spherical Bessel functions,
- Pℓ are Legendre polynomials, and
- the hat ^ denotes the unit vector.
In the special case where k is aligned with the z axis,
where θ is the spherical polar angle of r.