# What determines the usual chemistry textbook plots of atom orbitals?

In elementary chemistry textbooks you often have pictures like the following one:

Are there any conventions how to get them?

I am not sure, but I guess that it are contour plots with only one iso-surface of constant probability density $|\psi|^2$ such that the (integrated) probability for an electron to be inside of on the blue volumes, is 90 %.

If so, give those conditions a unique result and how to solve it numerically? Maybe you could add an example using python mayavi or something like that.

Note that my question is not of how to visualize the probability density via colormap or scatter plots, that's conceptually clear.

Did you check the Mayavi Example Atomic Orbital? If you remove the phase-coloring and find the additional parameter to contour that sets the cutoff, it produces the textbook plots.
• @student: there's an infinite amount of volumes that have probability = 0.9. Consider that there's a volume VA enclosed within this volume whose probability is 0.01, and a another volume VB outside this volume whose probability is also 0.01 (since there's still 10% chance for the electron to be outside this volume). Now If I construct a new volume by excluding VA and including VB, the probability of the electron being in this new volume is 0.9 - 0.01 + 0.01 = 0.9. In general, ∫∫∫ p(v) dV = P has no unique solution for 0<P<1 – MSalters Mar 21 '16 at 14:06