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- Why is [tex]\Delta l = \pm 1[/tex]? My book simply states this is due the angular momentum of photons, but we have that [tex]L_{photon} = \pm 1 \hbar[/tex] and [tex]L_{electron} = \sqrt{l(l+1)} \hbar[/tex]. The fact that l must change with one doesn't seem compatible...?

- (
*possibly*vague question, skip if confusing) What is the meaning of [tex]m_l[/tex] (measure for the projection of [tex]\vec L[/tex] on the z-axis) if we don't define a z-axis? Or in other words: sure we can always define a z-axis, but this can be totally arbitrary (assuming no external B-field or something), suggesting that due to symmetry it's true for every axis, but that is not true, so what is up with that?

- Why doesn't spin influence the spectral lines of certain atoms? I've read somewhere it's because sometimes the net spin of the atom is zero, but I don't see the relevance of that. For example: say we have an electron with spin up (and there's an external magnetic field) and it drops down from [tex]l=1,m_l=1[/tex] to [tex]l=0,m_l=0[/tex]. Now wouldn't we
*always*expect a different energy jump (and thus some other frequency of the emitted light) if the electron had spin down? (due to the external magnetic field)

- Trying to understand the Stern & Gerlach experiment: looking up silver, we see that its configuration is [tex](Kr) 4d^{10} 5s^{1}[/tex], so if I understand correctly the reason [tex]m_l[/tex] does not play a role in the experiment is because in the s-orbit, [tex]m_l = 0[/tex], and in the other orbits for every [tex]m_l[/tex] there's another one with the opposing sign? But there
*is*a net spin, resulting in the famous result of the experiment. Okay, that sounds understandable. This, however, means that quantummechanically, without the knowledge of spin, we would expect one line, i.e. no deviation (because net magnetic orbital number is zero). However, the experiment was to measure the quantization of [tex]L[/tex]: how were they planning to measure that? Or in other words: I don't understand what*they*(Stern & Gerlach) were expecting to see (which indicates I might be misunderstanding the whole experiment).

Thank you!