Radial wave-functions and spherical harmonics of p-orbitals in a certain hypothesis I know that the s-orbitals of H atom are spherically symmetrical. But the p,d or f orbitals aren't. So, the H-atom needn't necessarily be spherically symmetrical, as the wave-function would be a linear combination of all the orbitals. But, in a certain hypothesis, if I assume the H-atom to be spherically symmetrical, what could I possibly comment on the specific orientations of $p_{x}$, $p_{y}$ and $p_{z}$ orbitals in space? The radial and angular wave-functions might/mightn't change for the p-orbitals, but how to comment on their spatial orientations? Can someone help me out in this?
In &quot;real life&quot;, the hydrogen atom has its only electron in the s orbital. And unless it gets to an excitated state, that's the only thing that matters (whether you're studying the energy of the atom or the bounds it can make in terms of energy or symmetry).
Nevertheless, the H atom is likely to have a spherical symmetry, so any of its p-orbitals will be orthogonal to the others, so their linear combination is likely to keep the overall spherical(-ish) symmetry of the atom.
Here is a representation of such orbitals :

(Reference)
Hope this helps!