plotting - Is there something like DensityPlot3D to visualize atomic orbitals?

I'm visualizing some hydrogen like atomic orbitals. For looking at plane slices of the probability density, the DensityPlot function works well, and with something like:

Manipulate[
 DensityPlot[ psi1XYsq[u, v, z], {u, -w, w}, {v, -w, w} ,
  Mesh -> False, Frame -> False, PlotPoints -> 45,
  ColorFunctionScaling -> True, ColorFunction -> "SunsetColors"]
 , {{w, 10}, 1, 20}

 , {z, 1, 20, 1}
 ]

I can get a nice plot

I was hoping that there was something like a DensityPlot3D so that I could visualize these in 3D, but I don't see such a function. I was wondering how DensityPlot be simulated using other plot functions, so that the same idea could be applied to a 3D plot to construct a DensityPlot3D like function?

Answer

In the version 10.2, there is a builtin DensityPlot3D function, which can be used to visualize orbitals.

a0=1;

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]]

DensityPlot3D[(Abs@ψ[{3, 2, 0}, {Sqrt[x^2 + y^2 + z^2], 
     ArcTan[z, Sqrt[x^2 + y^2]], ArcTan[x, y]}])^2, {x, -10 a0, 
  10 a0}, {y, -10 a0, 10 a0}, {z, -15 a0, 15 a0}, 
 PlotLegends -> Automatic]

Or use ListDensityPlot3D:

data = Block[
 {nψ = 
   CompileWaveFunction[ψ[3, 1, 0, r, ϑ, φ]], data, vol},
 Table[Abs[nψ[x, y, z]]^2, {z, -20, 20, 0.25}, {y, -20, 20, 0.25}, {x, -20, 20, 0.25}]];

ListDensityPlot3D[data]

The function definition of the wave function is the same as in the other answer in this question.