Fonctions radiales de l' atome d' hydrogène

P Reinhardt, LCT, UPMC

Définitions

R10[r_]:=2(Z/a0)^(3/2)Exp[-Z r/a0]
R20[r_]:=1/Sqrt[8](Z/a0)^(3/2)(2-Z r/a0)Exp[-Z r/(2 a0)]
R30[r_]:=2/3(Z/(3a0))^(3/2)(3-2(Z r/a0)+2/9(Z r/a0)^2)Exp[-Z r/(3 a0)]
R21[r_]:=1/(2Sqrt[6])(Z/a0)^(3/2)(Z r/a0)Exp[-Z r/(2 a0)]
R31[r_]:=2Sqrt[2]/3(Z/(3a0))^(3/2)(2-(Z r/(3a0)))(Z r/(3a0))Exp[-Z r/(3a0)]
R32[r_]:=4/(3Sqrt[10])(Z/(3a0))^(3/2)(Z r/(3a0))^2Exp[-Z r/(3a0)]

Norme

Integrate[(r R31[r])^2,{r,0,∞},Assumptions->Z/a0>0]//Simplify

Graphes

Z=1;a0=1;

Plot[{(r R10[r])^2,(r R20[r])^2,(r R30[r])^2,(r R21[r])^2,(r R31[r])^2,(r R32[r])^2},{r,0,20},PlotRange->Full,AxesLabel->{"r en Bohr","[r R(r)]²"},AxesStyle -> Directive[Thick,15],PlotStyle->{{Blue,Thick},{Blue,Thick},{Blue,Thick},{Red,Dashed,Thick},{Red,Dashed,Thick},{Green,Thick}}]

Plot[(r R10[r])^2,{r,0,20},PlotRange->Full,AxesLabel->{"r en Bohr","[r R(r)]²"},AxesStyle -> Directive[Thick,15],PlotStyle->{{Blue,Thick},{Blue,Thick},{Blue,Thick},{Red,Dashed,Thick},{Red,Dashed,Thick},{Green,Thick}}]

Plot[{(r R20[r])^2,(r R21[r])^2},{r,0,20},PlotRange->Full,AxesStyle -> Directive[Thick,15],AxesLabel->{"r en Bohr","[r R(r)]²"},PlotStyle->{{Blue,Thick},{Red,Dashed,Thick}}]

Plot[{(r R30[r])^2,(r R31[r])^2,(r R32[r])^2},{r,0,20},PlotRange->Full,AxesStyle -> Directive[Thick,15],AxesLabel->{"r en Bohr","[r R(r)]²"},PlotStyle->{{Blue,Thick},{Red,Dashed,Thick},{Green,Dotted, Thick}}]