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Plane Wave Expansion
In physics, the plane wave expansion expresses a plane wave as a linear combination of spherical waves,
In the special case where k is aligned with the z-axis,
where ? is the spherical polar angle of r.
Expansion in spherical harmonics
With the spherical harmonic addition theorem the equation can be rewritten as
Note that the complex conjugation can be interchanged between the two spherical harmonics due to symmetry.
The plane wave expansion is applied in