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If we have a two electron system we can either have a singlet or triplet state.

The singlet state looks like

$$\chi=\frac{1}{\sqrt 2}(\chi_{+-}-\chi_{-+})$$

but we also have a triplet state in which

$$\chi=\frac{1}{\sqrt 2}(\chi_{+-}+\chi_{-+})$$

What is the physical difference between these two states due to the different phase factor?

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  • $\begingroup$ The triplet actually has three members: $\chi_{++},\frac{1}{\sqrt 2}(\chi_{+-}+\chi_{-+}),\chi_{--}$. It has angular and magnetic moment, the singlet state has none of these. $\endgroup$ – my2cts Apr 30 '18 at 21:50
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If you rotate the singlet it will remain the same. It has a total spin of 0.

If you rotate the triplet it will become a mixture of $\chi_{++}$, $\chi_{--}$, and ${1\over \sqrt 2}(\chi_{+-}+\chi_{-+})$. It has a total spin of 1.

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The singlet state is spin-0 when measured from any angle. In contrast, the triplet state will be seen as spin-0 when measured along the $z$-axis, but will be measured as spin-1 along an orthogonal axis (like the $x$-axis).

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