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Let's say there's a Hydrogen atom in a spin triplet state.

$$ | \downarrow\downarrow \rangle$$

Now let's say a photon with spin 1 came along abs was absorbed by the atom. We don't know if the proton or electron absorbed the atom, so they are now in a superposition.

$$\frac{1}{\sqrt{2}}\big(| \downarrow\uparrow \rangle+| \uparrow\downarrow \rangle \big)$$

If yet another photon spin 1 came along whichever one had spin down would absorb it and the result would be that both have spin up.

$$ | \uparrow\uparrow \rangle$$

That was a spin triplet state. But now let's consider a spin singlet state. The whole point of this state is that it cannot change into other spin states, right?

$$\frac{1}{\sqrt{2}}\big(| \downarrow\uparrow \rangle-| \uparrow\downarrow \rangle \big)$$

If this state cannot change then it must mean it cannot absorb nor emit photons with spin 1 or -1, but then, how does it interact with the electromagnetic force?

In fact this is similar to how color singlet states cannot absorb nor emit gluons, but the electromagnetic force is not confined like the Strong is, so singlet states must interact with electromagnetism somehow, right?. Perhaps it can absorb photons in some weird superposition of spin states?

I don't know, please help me out here.

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  • $\begingroup$ 'how color singlet states cannot absorb nor emit gluons' Well in fact there are gluons being emitted and absorbed constantly within colour singlet states. In a colour singlet state at any time there are its valence quarks, and a 'gluonic' sea of gluons and quark-anti quark pairs. However what I think you're saying is that colour singlet states do not interact via the strong force with coloured states and colourless as they are colourless but that does not pretain that they do not emit or absorbed gluons because internally this is happening constantly due to the vacummn fluctuations in QCD $\endgroup$ Apr 29, 2022 at 21:34
  • $\begingroup$ Are the particles that form the 2 spin states electrons? Do you mean helium? They could still interact by their charge. $\endgroup$
    – my2cts
    May 1, 2022 at 20:59

2 Answers 2

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The meaning of a spin singlet, in contrast with a triplet for instance, is that the singlet is invariant under rotations, while a triplet state that is rotated will in general be placed into some linear superposition of 3 basis states (the usual choice of 3 being $\lvert\uparrow \uparrow\rangle$, $\frac{1}{\sqrt{2}}(\lvert\uparrow \downarrow\rangle+ \lvert\downarrow \uparrow\rangle)$, and $\lvert\downarrow\downarrow\rangle$). This is mathematically equivalent to the statement that the singlet has an overall spin of 0, while the triplet has an overall spin of 1.

Any statement that a singlet "can't change" only means that it remains in the same state after a rotation; it doesn't mean that it can't be affected by a physical process. Indeed, a singlet state can turn into a triplet state or vice versa by absorbing or emitting a photon.

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There are many issues with this question. Firstly, hydrogen has only one electron. It does not have singlet or triplet states. Then it is proposed to consider a dipole singlet-triplet transition, which hoever is dipole forbidden.

A dipole transition requires a change in orbital angular momentum, not in spin.

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