I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this:
I can plot 4 overlapping probability densities in a tetrahedral shape:
So far it looks OK. But when I'm trying to sum the orbitals (wavefunctions) and square the resulting function to get the probability density, I always come up with a sphere:
So I have the following questions:
1.) Is this an expected result? If not, what am I doing wrong?
2.) What is usually depicted on the sp3-hybridization schemes: overlapping wavefunctions, sums of the wavefunctons, probability density or something else?