Spherical Harmonics

In this Mathematica Notebook we investigate the size of the spherical harmonics, by plotting the surface (r sin(ϕ) sin(θ), r cos(ϕ) sin(θ), cos(θ))with r=|(Subscript[Y, L M])(θ,ϕ)|. This just shows the size of the spherical harmonic. The function plY plots the (Subscript[Y, L M])(θ,ϕ). You can investigate this yourself, or look at the prepared pictures for various values of L, by double clicking on the lines with the triangles at the bottom at the right.

Definition of plY

plY[l_,m_]:=ParametricPlot3D[Abs[SphericalHarmonicY[l,m,θ,ϕ]]{Sin[θ]Sin[ϕ],Sin[θ]Cos[ϕ],Cos[θ]},{θ,0,π},{ϕ,0,2π}]

L=0

(Subscript[Y, 00])

plY[0,0]

L=1

(Subscript[Y, 10])

plY[1,0]

(Subscript[Y, 11])

plY[1,1]

L=2

(Subscript[Y, 20])

plY[2,0]

(Subscript[Y, 21])

plY[2,1]

(Subscript[Y, 22])

plY[2,2]

Even Higher order, L=5

(Subscript[Y, 50])

plY[5,0]

(Subscript[Y, 55])

plY[5,5]