I have been calculating probability density functions for different states in the hydrogen atom, and want to plot them in 3D using a dot density plot like this one. However, I have not figured out how to convert my function into a list distribution that can be plotted using a density plot. Here are the three functions I’ve been working on.

```
probs=
{(E^(-2 Im(ArcTan(x, y)) - Re(Sqrt(x^2 + y^2 + z^2))) Abs(x^2 + y^2))/(896 (Pi)),
(2 E^(2 Im(ArcTan(x, y)) - 2/3 Re(Sqrt(x^2 + y^2 + z^2))) Abs(Sqrt(x^2 + y^2) z)^2)/(45927 (Pi)),
(3 E^(-4 Im(ArcTan(x, y)) - 1/2 Re(Sqrt(x^2 + y^2 + z^2))) Abs((x^2 + y^2) (-12 + Sqrt(x^2 + y^2 + z^2)))^2)/(29360128 (Pi))}
```

These are each for the states |211>, |32,-1>, |422>.