SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/HydrogenAtom"]

Model of the Hydrogen Atom

pdf[l_,m_,n_][ρ_,ϕ_,θ_]:=(α^3)Factorial[n-l-1]/(2n Gamma[n+l+1])Exp[-α ρ](((α ρ))^(2l))((LaguerreL[n-l-1,2l+1,α ρ])^2)SphericalHarmonicY[l,m,ϕ,θ]Conjugate[SphericalHarmonicY[l,m,ϕ,θ]]

pdf[l,m,n][ρ,ϕ,θ]//FullSimplify

pdf[0,0,1][ρ,ϕ,θ]/.α->1//FullSimplify

pdf[2,0,3][Sqrt[(x^2)+(y^2)+(z^2)],ArcCos[z/Sqrt[(x^2)+(y^2)+(z^2)]],ArcTan[x,y]]/.α->1

SliceDensityPlot3D[pdf[2,0,3][Sqrt[(x^2)+(y^2)+(z^2)],ArcCos[z/Sqrt[(x^2)+(y^2)+(z^2)]],ArcTan[x,y]]/.α->1,"CenterPlanes",{x,-10,10},{y,-10,10},{z,-10,10},AxesLabel->{"\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["x", "TI"], TraditionalForm], "errors" -> {}, "input" -> "x", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["y", "TI"], TraditionalForm], "errors" -> {}, "input" -> "y", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["z", "TI"], TraditionalForm], "errors" -> {}, "input" -> "z", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"},PlotPoints->50,BaseStyle->FontSize->12]

SliceContourPlot3D[pdf[2,0,3][Sqrt[(x^2)+(y^2)+(z^2)],ArcCos[z/Sqrt[(x^2)+(y^2)+(z^2)]],ArcTan[x,y]]/.α->1,"CenterPlanes",{x,-10,10},{y,-10,10},{z,-10,10},AxesLabel->{"\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["x", "TI"], TraditionalForm], "errors" -> {}, "input" -> "x", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["y", "TI"], TraditionalForm], "errors" -> {}, "input" -> "y", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["z", "TI"], TraditionalForm], "errors" -> {}, "input" -> "z", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"},PlotPoints->50,BaseStyle->FontSize->12]

Export["hydrogenl2m0n3.pdf",%,"PDF"]

Export["hydrogenl2m0n3.eps",%%,"EPS"]