Kugelflächenfunktionen (Subscript[Y, lm])

<< Graphics`Graphics`
<< Graphics`Shapes`
<< Graphics`ParametricPlot3D`

(Subscript[Y, 10]) := SphericalHarmonicY[1, 0, θ, φ]

(Subscript[Y, 11]) := SphericalHarmonicY[1, 1, θ, φ]

(Subscript[Y, 1 - 1]) := 
      SphericalHarmonicY[1, -1, θ, φ]

(Subscript[Y, a]) = 1/Sqrt[2] Simplify[(Subscript[Y, 11]) - (Subscript[Y, 1 - 1])];

\(\(\(Y\_a\^*\) = 
        1/Sqrt[2]\ Simplify[
            Conjugate[Simplify[Y\_11 - Y\_\(1 - 1\)]]];\)\)

(Subscript[Y, b]) = 1/Sqrt[2] Simplify[(Subscript[Y, 1 - 1]) - (Subscript[Y, 11])];

\(\(\(Y\_b\^*\) = 
        1/Sqrt[2] Conjugate[Simplify[Y\_\(1 - 1\) - Y\_11]];\)\)

Integrate[
      Integrate[
        Abs[(Subscript[Y, a])]^2 Sin[θ], {θ, 0, π}], {φ, 0, 
        2 π}]

Integrate[
      Integrate[
        Abs[(Subscript[Y, b])]^2 Sin[θ], {θ, 0, π}], {φ, 0, 
        2 π}]

SphericalPlot3D[
      Abs[(Subscript[Y, 10])]^2, {θ, 0, π}, {φ, 0, 2 π}, 
      ImageSize -> 250]

ContourPlot[
      Abs[(Subscript[Y, 10])]^2 ,  {θ, 0, π}, {φ, 0, 2 π}, 
      ImageSize -> 250, ContourLines -> False]

SphericalPlot3D[
      Abs[(Subscript[Y, a])]^2 ,  {θ, 0, π}, {φ, 0, 2 π}, 
      ImageSize -> 250]

ContourPlot[
      Abs[(Subscript[Y, a])]^2 ,  {θ, 0, π}, {φ, 0, 2 π}, 
      ImageSize -> 250, ContourLines -> False, 
      PlotPoints -> 100]