- #1

Amok

- 256

- 2

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 :)