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This tag should be applied to questions that deal with the particular arrangement of atoms in a molecule, the so-called molecular structure or geometry.
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How do the spin-matrices change in systems without spherical symmetry?
The (non-relativistic) spin matrices of a free electron, with $z$ as the quantization axis, read:
$$
\boldsymbol{S}_{x}=\frac{\hbar}{2}\left[\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right], \quad …