# Whats the difference between a symmetric and antisymettric two electron system with both spins pointing in different directions?

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?

• 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. Commented Apr 30, 2018 at 21:50

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.
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).