I just studied atomic orbitals in a theoretical QM class, and I'm left with several questions, that are probably more questions in quantum chemistry:
- Many orbitals seem to have a preferred axis - how is that axis "chosen"? Does it move constantly, or is it actually a fixed direction in space? Why is there an axis at all when the problem is spherically symmetric? Does the shape of the orbitals have any bearing on chemistry?
- We can see lobes in preferred directions - do these actually play a role in chemical reactions, or maybe in crystallography for the arrangement of crystals?
- If I understand correctly, electrons are actually represented by superpositions of spherical harmonics - with an arbitrary superposition, the probability density for the electron could be anything - can we actually find the coefficients of the superposition an electron actually is in?
- Lastly, there is an orbital which has a high probability of the electron being at the center of the nucleus (I don't remember which one) - is that anything interesting?