Problem with SphericalPlot3D plotting

Question

I want to plot the real part of the SphericalHarmonicY[1,1,θ,φ]. That is, I want to plot

$$ - \frac{1}{2}\sqrt {\frac{3}{{2\pi }}} \cos[\phi ]\sin[\theta ]$$

To do so, I evaluated the following expression:

SphericalPlot3D[-(1/2) Sqrt[3/(2 π)] Cos[φ] Sin[θ], {θ, 0, π}, {φ, 0, 2 π}]

But the result I got doesn't show the negtive part. What is wrong?

Answer 1

The negative part is plotted with negative radius, so it's at the opposite position of where you expect it -- it's exactly overlapping the positive part. You'll have to plot its absolute value or its square, as Nasser suggests, and indicate its negativeness using a different colour or something. Here's one way to do it:

f[θ_, φ_] := -(1/2) Sqrt[3/(2 π)] Cos[φ] Sin[θ]
pos[x_] := If[x >= 0, x, Null]
SphericalPlot3D[{pos[f[θ, φ]], pos[-f[θ, φ]]},
 {θ, 0, π}, {φ, 0, 2 π}, 
 PlotStyle -> {Lighter@Lighter@Red, Lighter@Lighter@Blue}, 
 Lighting -> "Neutral"]