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Δframe=−ℏω0⟨σz⟩/2\Delta_{\rm frame} = -\hbar\omega_0\langle\sigma_z\rangle/2

Why this formula appears here

the detuned Hamiltonian that governs spin precession in a frame rotating with an applied field — the identical construction I. I. Rabi used to analyze spin behavior in a gyrating magnetic field in 1937 [ 14 ] . Two checks confirm the recovery is exact rather than incidental: at ωr\omega_r = 0 , the non-rotating case, Δframe\Delta_{\rm frame} ≡\equiv 0 and HcH_c = HfH_f , the already-verified baseline; at ωr\omega_r = ω0\omega_0 , exact corotation, HcH_c = 0 and the spin’s energy in this frame vanishes identically, which is the ordinary resonance condition, not a puzzle, because Δframe\Delta_{\rm frame} = -ℏ\hbarω0\omega_0⟨\langleσz\sigma_z⟩\rangle/2 exactly cancels the lab-frame value for a state that starts, and stays,…

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Δframe\Delta_{\rm frame}

Symbol Delta_rm frame

Deltara_rm frame is part of the quantity the equation computes from the expression on the right.

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ω0\omega_0

Symbol omega_0

omega0a_0 is one of the signed contributions combined to compute the quantity on the left.

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σz\sigma_z

Symbol sigma_z

sigmaza_z is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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Δframe=−ℏω0⟨σz⟩/2\Delta_{\rm frame} = -\hbar\omega_0\langle\sigma_z\rangle/2

Equation 137 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

the detuned Hamiltonian that governs spin precession in a frame rotating with an applied field — the identical construction I. I. Rabi used to analyze spin behavior in a gyrating magnetic field in 1937 [ 14 ] . Two checks confirm the recovery is exact rather than incidental: at ωr\omega_r = 0 , the non-rotating case, Δframe\Delta_{\rm frame} ≡\equiv 0 and HcH_c = HfH_f , the already-verified baseline; at ωr\omega_r = ω0\omega_0 , exact corotation, HcH_c = 0 and the spin’s energy in this frame vanishes identically, which is the ordinary resonance condition, not a puzzle, because Δframe\Delta_{\rm frame} = -ℏ\hbarω0\omega_0⟨\langleσz\sigma_z⟩\rangle/2 exactly cancels the lab-frame value for a state that starts, and stays,…

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