Funções de onda do átomo de H - parte radial

L=0

a0=Quantity["BohrRadius"]/Quantity["Meters"]

ψ[{n_,l_,m_},{r_,θ_,ϕ_}]:=With[{ρ=2 r/(n a0)},Sqrt[(2/(n a0))^3 (n-l-1)!/(2 n (n+l)!)] Exp[-ρ/2] ρ^l LaguerreL[n-l-1,2 l+1,ρ] SphericalHarmonicY[l,m,θ,ϕ]]

n=2;l=0;m=0

Integrate[ψ[{n,l,m},{r,θ,ϕ}]*Conjugate[ψ[{n,l,m},{r,θ,ϕ}]]r^2 Sin[θ],{r,0,Infinity},{θ,0,Pi},{ϕ,0,2Pi}]

Integrate[Abs[ψ[{n,l,m},{r,θ,ϕ}] ]^2  r^2 Sin[θ],{r,0,Infinity},{θ,0,Pi},{ϕ,0,2Pi}]

φr[{n_,l_},r_]:=With[{ρ=2 r/(n a0)},Sqrt[(2/(n a0))^3 (n-l-1)!/(2 n (n+l)!)] Exp[-ρ/2] ρ^l LaguerreL[n-l-1,2 l+1,ρ]]

Plot[Evaluate[Table[φr[{n,0},r],{n,1,5}]],{r,0,10a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-3 10^14,10^15}]

Plot[Evaluate[Table[r φr[{n,0},r],{n,1,5}]],{r,0,10a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-10^5,10^5}]

Plot[Evaluate[Table[r φr[{n,0},r],{n,1,5}]],{r,0,50a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-10^5,10^5}]

n=5

Plot[Evaluate[Table[r φr[{5,l},r],{l,0,4}]],{r,0,50a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-0.5 10^5,0.5 10^5}]

Plot[Evaluate[Table[r φr[{5,l},r],{l,0,4}]],{r,0,10a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-2 10^4,2 10^4}]

Todos os momentos angulares para um dado n

Manipulate[Plot[Evaluate[Table[r φr[{n,l},r],{l,0,n-1}]],{r,0,maximo a0},PlotStyle->{Red,Blue,Green,Black,Pink,Gray,Cyan,Magenta,Brown,Orange,Purple},PlotRange->{-ymax,ymax},PlotLabels->Range[0,n-1]],{{n,5},1,10,1} ,{{maximo,10},1,50},{{ymax,2 10^4},10^3,10^6}]

Todos os n para momento angular 0

Manipulate[Plot[Evaluate[Table[r φr[{n,0},r],{n,1,nmax}]],{r,0,maximo a0},PlotStyle->{Red,Blue,Green,Black,Pink,Gray,Cyan,Magenta,Brown,Orange},PlotRange->{-ymax,ymax},PlotLabels->Range[1,nmax]],{{nmax,5},1,10,1} ,{{maximo,10},1,50},{{ymax,2 10^4},10^3,10^6}]

Plot[Evaluate[Table[r φr[{n,0},r],{n,1,5}]],{r,0,10a0},PlotStyle->{Red,Blue,Green,Black,Pink},PlotRange->{-10^5,10^5}]