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What is meant with the term "triplet state"? I find it strange to call a space spanned by three degenerate states as if it was a single state. If you were asked to give a mathematical description of the term triplet state, what would you write down?

I would think that a proper representation is a density operator of the form $$ \rho_T = \frac{1}{3}\big (|{-1}\rangle \langle {-1}| + |0\rangle \langle 0|+|1\rangle \langle 1| \big) $$ where $|n\rangle$ stands for a state with $m_s=n$, them having the same energy is implied.

But that is not a single state or is it? For a single state I would expect to be able to write it down as a single state vector of the form $$ |T\rangle= \cdots $$ but that would not be correct since that is not the same as the density operator. So how should one understand the term "triplet state"?

Am I wrong to interpret the word "state" to mean a pure state that can be defined by a single state vector?

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I don't think anyone is calling the space of spin-1 states the "triplet state". Rather, a triplet state (note the indefinite article) is any pure state that lies in the three-dimensional space of spin-1 states, and perhaps more generally any mixed state consisting only of states from that space.

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  • $\begingroup$ There are publications that literally call it the triplet state. The Triplet State and Molecular Electronic Processes in Organic Molecules, doi.org/10.1021/cr60240a004, also The Triplet state pubs.acs.org/doi/pdf/10.1021/ed046p2 It sounds to me as if the triplet state is on the same footing as the singlet state. The distinction is not obvious if one isn't already familiar with the topic. $\endgroup$
    – Hans Wurst
    Dec 15, 2021 at 15:47
  • $\begingroup$ @HansWurst I'm not sure what your point here is - your second reference does exactly what I claim in this answer in its paragraph appropriately titled "Definition of a Triplet State" [emphasis mine]. Although there is some weird formulations in there, this seems at most like an idiosyncratic usage of terminology by chemists (both papers you linked are chemistry papers, not physics papers), not any disagreement over the underlying physics. $\endgroup$
    – ACuriousMind
    Dec 15, 2021 at 15:59
  • $\begingroup$ Inaccurate usage is very prevalent in chemistry and mightily confusing especially for people that never have a proper exposition like physicists. Which is why I'd like a crystal clear statement how to use the term and what it does(should) mean and what it does not mean. Aren't the titles of these papers strictly speaking nonsense ? As you said yourself there isn't "the" triplet state. But I've had discussions with chemists that use the term as if it was a singular electronic state. They did it so naturally, as if it was self evident to use it in such a way, that I started to have doubts. $\endgroup$
    – Hans Wurst
    Dec 15, 2021 at 17:06
  • $\begingroup$ @HansWurst I'm confident that what I say in my answer is true for the usage of the term in ordinary physics. I cannot force chemists (or anyone really) to comply ;) $\endgroup$
    – ACuriousMind
    Dec 15, 2021 at 17:09
  • $\begingroup$ Your shortcomings are noted. But don't worry, providing good answers here makes more than up for that :-0 $\endgroup$
    – Hans Wurst
    Dec 15, 2021 at 18:11

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