Im trying to plot the results of the schroedinger equation for hydrogen in mathematica
this is the function I defined:
Wavefunction[r_, w_, a_, n_, l_, m_] := LaguerreL[n - l - 1, 2*l + 1, 2*r/n]*LegendreP[l, m, Cos[w]]* E^(I*m*a)*Sqrt[((2*l + 1)*(l - m)!)/(4*Pi *(l + m)!)]* E^-(r/(n))*(2*r/(n))^l* Sqrt[(2/(n))^3*(n - l - 1)!/(4*Pi*(n + l)!)]
Its a bit messy and not necessarily fault free yet, but It doesnt really change my question much. What would be a smart way of plotting this function. its in spherical coordinates, n l and m are quantum numbers, r the radius w and a are angles, LaguerreL and LegendreP are built in functions.
I looked at contourplots and density plots, But I cant come up with a statisfying result in spherical coordinates (and way to display the resulting wavefunctions with say cutouts or translucency)
ps: this is basically what I hope to plot. the electron orbitals of hydrogen: hydrogen orbitals