Hydrogen Atom

$Assumptions={ec > 0, μ > 0, ℏ > 0, r>0}

a=4 π ϵ (ℏ^2)/((ec^2) μ)

Rf=Exp[-r/a]

D[Rf,{r,2}]

energy=Simplify[(((-(ℏ^2))/(2μ))(D[Rf,{r,2}]+(2/r)D[Rf,r])-((ec^2)/(4π ϵ r ))Rf)/Rf]

energy *a

Rf=(1-r/(2 a)) Exp[-r/(2a)]

energy=Simplify[(((-(ℏ^2))/(2μ))(D[Rf,{r,2}]+(2/r)D[Rf,r])-((ec^2)/(4π ϵ r ))Rf)/Rf]

energy * a

Solve[D[(r^2)((Exp[-r/a0])^2),r]==0]

p10[r_]:=((Exp[-r])^2) (r^2)

Plot[p10[r],{r,0,5}]

Solve[D[(r^2)(((2-r/a0))^2)((Exp[-r/(2a0)])^2),r]==0]

N[%]

p20[r_]:= (((2-r))^2)((Exp[-r/2])^2)  (r^2)

Plot[p20[r],{r,0,12}]

N[Solve[D[((((r/a0)))^2)((Exp[-r/(2a0)])^2)(r^2),r]==0]]

p21[r_]:= (((r))^2)((Exp[-r/2])^2)  (r^2)

Plot[p21[r],{r,0,12}]