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I was thinking about how the S_{z}operator "couples" (has non zero matrix elements) states with the same expectation values for the projection of spin on the z-axis (duh! α and β are its eigenvectors), and how S_{x}and S_{y}couple different states (once again, duh!). I was also thinking that this would hold for a two-particle system, i.e. that triplet states would couple to singlet states. I sat down and wrote down the expressions for the operators in a two-particle space (4-by-4 matrices) in both the "usual" basis (αα, αβ, βα, ββ) and the basis consisting of the singlet state+triplet states. I found that the singlet state does not "couple" to any other state through S_{x}or S_{y}, which if found to be counterintuitive. Do you see an inherent flaw in my reasoning? Do you think my conclusions are correct?

For reference, a lot of the expressions for the operators are found here:

http://electron6.phys.utk.edu/qm1/modules/m10/twospin.htm

Thank you in advance and all the best :)

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# Two spin 1/2 partcles and spin operators

Can you offer guidance or do you also need help?

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