# Can atomic orbitals of an isolated atom rotate relative to the nucleus?

I am a beginner at orbitals. It seemed interesting to me while studying p orbitals that the texts don't suggest that the orbitals are rigid relative to the nucleus.

But I thought mathematically these rotations would not be possible to know because the wave function of the orbitals only tell about the probability. Until this:(Simple rotation of an atomic orbital wavefunction)( I didn't understand it as I don't know the mathematics; I am trying)

So, is it possible for orbitals to rotate relative to the nucleus? If yes, what validates it; if no, what disallows it?

• What do you mean by the oribitals "rotating"? By definition, the orbitals are stationary states, i.e. they do not change in time. – ACuriousMind Dec 9 '16 at 15:45
• Maybe I missed that point. Then what does rotation mean in that question? What prohibits their 'movement'? – Partha Sarker Dec 9 '16 at 16:11
• I presume you've been looking at some set of visualizations—the pictures that show p-orbitals as dumbbell shapes, say. There are at least two ways to interpret this question in it's current form: (a) do the dumbbells have to be lined up on the axes as they are usually shown (answer, no the choice of axes is arbitrary) and (b) if I know that an electron exists in p-orbital that is currently lined up with the x-axis and look again a little later could I find it in a dumbbell at an angle with the x-axis. The second question is not very well posed, but as @ACuriousMind's comment say "no". – dmckee --- ex-moderator kitten Dec 9 '16 at 17:09

Atomic p orbitals have angular momentum. The angular part of the wavefunction is described by the spherical harmonics $Y_{\ell,m}$ where $\ell=1$ and $m=-1,0,1$. When one multiplies this with the time-dependent part $e^{iEt/\hbar}$, the result is a rotating phase.
The $p_x$ and $p_y$ orbitals of chemical compounds are different linear combinations of $Y_{1,1}$ and $Y_{1,-1}$ without angular momentum along the z-axis.
Absorption of linearly polarized light may transfer an electron from an $s$ orbital to a $p_x$ orbital, but it will not remain oriented because of spin-orbit coupling.