# Plotting a 4dimensional spherical function In mathematica [duplicate]

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

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• The choice is very much a matter of taste. – bbgodfrey Apr 6 '15 at 19:14
• – chris Apr 6 '15 at 19:53
• I looked at thatone, but I couldnt get the nuts and bolts too match, mainly due to this being in spherical coordinates – catadoxas Apr 6 '15 at 19:55