Representando as funções de onda angulares

Fórmulas analíticas

SphericalHarmonicY[3,2,θ,ϕ]

SphericalHarmonicY[3,2,θ,ϕ] //ExpToTrig

LegendreP[3,3,x]

Gráficos 3D

Manipulate[SphericalPlot3D[Evaluate[SphericalHarmonicY[l,m,θ,ϕ] SphericalHarmonicY[l,-m,θ,ϕ]],{θ,0,Pi},{ϕ,0,2Pi},PerformanceGoal->"Quality",AspectRatio->Automatic],{l,0,7,1},{m,0,l,1}]

Manipulate[SphericalPlot3D[Evaluate[LegendreP[l,m,Cos[θ]] ^2],{θ,0,Pi},{ϕ,0,2Pi},PerformanceGoal->"Quality",AspectRatio->Automatic],{l,0,7,1},{m,0,l,1}]

Manipulate[SphericalPlot3D[Evaluate[Re[SphericalHarmonicY[l,m,θ,ϕ] ]],{θ,0,Pi},{ϕ,0,2Pi},PerformanceGoal->"Quality",AspectRatio->Automatic],{l,0,7,1},{m,0,l,1}]

Gráfico da parte θ do harmônico esférico

Manipulate[ Plot[LegendreP[l,m,Cos[θ]],{θ,0,Pi}],{l,0,7,1},{m,0,l,1}]