Quelques orbitales de l' atome d' hydrogène

Clear["Global`*"]

Coordonnées polaires

r[x_,y_,z_]:=Sqrt[x*x+y*y+z*z]

x[r_,θ_,ϕ_]:=r Sin[θ]Cos[ϕ]
y[r_,θ_,ϕ_]:=r Sin[θ]Sin[ϕ]
z[r_,θ_,ϕ_]:=r Cos[θ]

Définitions

Orb1scart[x_,y_,z_]:=Exp[-r[x,y,z]]
Orb2pzcart[x_,y_,z_]:=z Exp[-r[x,y,z]/2]
Orb3dxycart[x_,y_,z_]:=x y Exp[-r[x,y,z]/3]//Simplify
Orb1scart[x,y,z]

Orb1sspher[r_,θ_,ϕ_]:=Exp[-r]
Orb2pzspher[r_,θ_,ϕ_]:=z[r,θ,ϕ] Exp[-r/2]
Orb3dxyspher[r_,θ_,ϕ_]:=x [r,θ,ϕ] y[r,θ,ϕ]  Exp[-r/3]//Simplify

Normalisation

Integrate[Orb3dxycart[x,y,z]^2, {x,-∞,∞},{y,-∞,∞},{z,-∞,∞}]

Integrate[Orb3dxyspher[r,θ,ϕ]^2 r^2 Sin[θ], {r,0,∞},{θ,0,π},{ϕ,0,2π}]

Integrate[Orb1sspher[r,θ,ϕ]^2r^2Sin[θ], {r,0,Infinity},{ϕ,0,2Pi},{θ,0,Pi}]

Integrate[Orb2pzspher[r,θ,ϕ]^2r^2Sin[θ],{r,0,Infinity},{ϕ,0,2 Pi},{θ,0,Pi}]

Plot en 3 D

ContourPlot3D[Orb1scart[x,y,z]^2==0.01,{x,-10,10},{y,-10,10},{z,-10,10}]

ContourPlot3D[Orb2pzcart[x,y,z]^2==0.01,{x,-10,10},{y,-10,10},{z,-10,10}]

ContourPlot3D[Orb3dxycart[x,y,z]^2==2,{x,-10,10},{y,-10,10},{z,-10,10}]