3 upvotes, 1 direct replies (showing 1)
View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
Orbitals?! A recent thread on r/askscience raised some interesting points from comments that I never got closure one.
Are the orbitals spherical harmonics? If so, and with HUP, is there truly no pure state, e.g. 3s, rather, an infinite sum of weighted harmonic terms? Akin to Fourier terms for example.
Comment by wnoise at 06/12/2023 at 19:33 UTC*
10 upvotes, 0 direct replies
For single-electron atoms, they really are spherical harmonics. Things get more complicated for multiple electron atoms, but the spherical harmonics remain a reasonably good approximate description. For molecular orbitals, spherical harmonics are often not good descriptions, but the "hybrid" orbitals from perturbation theory are.
The spherical harmonics have HUP uncertainty already built in by being delocalized and having a spread of momentum -- no need to sum over many (though in situations like multi-electron atoms and small molecules, it may still be a nice basis to expand over and do computations in).