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So, the set-up is just degenerate perturbation theory for constant electric field along z on the n = 2 hydrogen states. That's a classic, so i don't have a problem with it: states [200] and [210] emerge in linear combinations, with energy levels split at ±3u (u = Bohr radius times eE) from the n = 2 level. [21±1] are unaffected.

Penultimate question is: "Assuming that the atom is in its ground state and the light is polarized in z- direction, determine frequencies of spectral lines in the absorption spectrum, which will be observed, and their relative strength"

That doesn't seem hard either: jumps from the ground state imply absorption of ΔE or ΔE±3u, where ΔE is the energy difference between ground state and n = 2; frequency is given by E = hf. Then ΔE absorption should be twice the intensity of any of the two others.

Finally the one i'm stuck on: "

**Can Stark effect be observed with x-polarized light? Give arguments based on Wigner- Eckart theorem**"

First of all, what's the deal about x-polarized here and why does it make a difference?

Then, it seems like the electric field ruins the spherical symmetry so how can we use Wigner-Eckart at all?

Maybe just on the [21±1] states?

If we can use it, then how?...Is it the selection rules that prevent [21±1] from being affected?

Thank you in advance..