Hydrogen wave functions.

Mathematica has an easier time plotting these if you leave off the normalization.  These are all plotted for r = 1.  See what happens if you change that.  Also, I' ve set a0, the Bohr radius to 1.

Hydrogen[n_,l_,m_,r_,th_,ph_] = Exp[-r/n](2 r/n)^l  LaguerreL[n-l-1,2 l+1,2 r/n] SphericalHarmonicY[l,m,th,ph]

SphericalPlot3D[Abs[Hydrogen[2,1,1,1,th,ph]],{th,0,Pi},{ph,0,2 Pi}, Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[2,0,0,1,th,ph]],{th,0,Pi},{ph,0,2 Pi},Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,1,1,1,th,ph]],{th,0,Pi},{ph,0,2 Pi},Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,1,1,1,th,ph]],{th,0,Pi},{ph,0,2 Pi}, Mesh->None,Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,1,1,1,th,ph]],{th,0,Pi},{ph,0,Pi},Mesh->None,Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,2,1,1,th,ph]],{th,0,Pi},{ph,0,Pi}, Mesh->None,Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,2,1,1,th,ph]],{th,0,Pi},{ph,0,2Pi}, Mesh->None,Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,2,0,1,th,ph]],{th,0,Pi},{ph,0,2Pi},Boxed->False,Axes->None]

SphericalPlot3D[Abs[Hydrogen[3,2,-1,1,th,ph]],{th,0,Pi},{ph,0,2Pi},Boxed->False,Axes->None]

Radial wavefunctions.  Remember, these are not normalized.  Compare to figure 4.4 in the book.

Plot[{Hyrdogen[1,0,0,r,0,0],Hydrogen[2,0,0,r,0,0],Hydrogen[3,0,0,r,0,0],Hyrdogen[1,1,0,r,0,0],Hydrogen[2,1,0,r,0,0],Hydrogen[3,1,0,r,0,0],},{r,0,10},PlotRange->All]