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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
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
See also
References