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Commuting operators share a common eigenbasis, so for a symmetry S of a Hamiltonian H, meaning [H,S ] = 0, ifH|ψ⟩ =E|ψ⟩ then we must also 8 haveS|ψ⟩ =s|ψ⟩ for some eigenvalues ofS

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2025 1

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