Quantum question - spinor singlet and triplet states - why are they significant and what can they tell us about an atom?

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Quantum question - spinor singlet and triplet states - why are they significant and what can they tell us about an atom?

Physics
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Consider the two electrons in a chemical bond. They have spin vectors and . Each of the components of the spin vector is quantized and can take on values . We now ask what are the allowed total spin states generated by adding the spins . If the two vectors are completely anti-parallel, i.e. , then the total spin , i.e. the magnitude of the total spin is 0. In this case, the only allowed value of the quantum number is 0. However, if any of the components of and are the same, the total spin will be a nonzero vector. Due to requirements of normalization, the only allowable nonzero value of the total spin is in magnitude, which leaves three possible values for , namely -1,0,1. For this reason, spin states in which the electrons have a total spin of magnitude are called the triplet states, while the one spin state corresponding to a total spin of 0 is called the singlet state.

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