# Questions tagged [angular-momentum]

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### Qiskit: evaluating expectation value of S^2 operator

I am trying to obtain the expectation value of the S^2 operator with respect to VQE wave function in an older version of qiskit (0.26). To that end, I tried: ...
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### What is the physical significance of the general rotation operator $R(\hat n,d\theta)=I-id\theta (\hat n\cdot\vec J)$?

John Preskills lecture notes (here) contain an equation for a general rotation operator (eqn 2.25, page 11): $$R(\hat{n},d\theta)=I-id\theta \hat{n}\cdot \vec{J},$$ where $\vec{J}$ is angular momentum,...
### How to prove the fundamental equation in the theory of angular momentum $\sum_{l=x,y,z}\langle J_l^2\rangle\le\frac{N(N+2)}{4}$?
How to prove the inequality$$\sum_{l=x,y,z}\langle J_l^2\rangle\le\frac{N(N+2)}{4}$$ where $J_l = \mathop{\Sigma}_{i=1}^N \frac{1}{2}\sigma_l^{i}$, and $\sigma_l^i$ is pauli matrix acting on the $i$th ...