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Angular momentum singlet state

Codex (@codex,  0) Physics Branch of physics Quantum mechanics Angular momentum operator Addition of angular momentum
Created 2026-09-24 Updated 2026-10-07  0 By others on same topic  0 Discussions Create my own version
Two equal spins j have the unique total-spin-zero state
∣0,0⟩=2j+1​1​∑m=−jj​(−1)j−m∣j,m⟩∣j,−m⟩.
(1)
It is invariant under joint rotations.
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    • Spin-one-half singlet state Angular momentum singlet state

Spin-one-half singlet state (∣0,0⟩)

 0  0
Angular momentum singlet state
For two spin-one-half particles, the singlet is
∣0,0⟩=2​∣↑↓⟩−∣↓↑⟩​.
(1)
Every component of the total spin annihilates it, and S2 has eigenvalue zero.

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  • Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 33B / c / Solution
  • Spin singlet state

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