(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using the orthonormality of [itex]|+\rangle[/itex] and [itex]|-\rangle[/itex], prove

[itex][S_i,S_j]= i \varepsilon_{ijk}S_k[/itex]

where

[itex]S_x = \frac{\hbar}{2}|+\rangle \langle - | + | - \rangle \langle + |[/itex]

[itex]S_y = -\frac{i\hbar}{2}|+\rangle \langle - | + | - \rangle \langle + |[/itex]

[itex]S_z = \frac{\hbar}{2}|+\rangle \langle + | - | - \rangle \langle - |[/itex]

3. The attempt at a solution

Since S_x and S_y commute, their commutator should be zero which contradicts [itex][S_x,S_y]= i S_z[/itex]. What am I missing here?

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# Homework Help: Sakurai Chapter 1 Question 8

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