Published equation contexts

$\omega_r = \omega_0$

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 $\omega_r$ = 0 , the non-rotating case, $\Delta_{\rm frame}$ $\equiv$ 0 and $H_c$ = $H_f$ , the already-verified baseline; at $\omega_r$ = $\omega_0$ , exact corotation, $H_c$ = 0 and the spin’s energy in this frame vanishes identically, which is the ordinary resonance condition, not a puzzle, because $\Delta_{\rm frame}$ = - $\hbar$ $\omega_0$ $\langle$ $\sigma_z$ $\rangle$ /2 exactly cancels the lab-frame value for a state that starts, and stays,…

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\omega_r

Symbol omega_r

omeg $a_r$ is part of the quantity the equation computes from the expression on the right.

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\omega_0

Symbol omega_0

omeg $a_0$ is an input to the expression that computes the quantity on the left.

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How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

[14] Space Quantization in a Gyrating Magnetic Field ↗

Published contexts (1)

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\omega_r = \omega_0

Equation 135 · 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 $\omega_r$ = 0 , the non-rotating case, $\Delta_{\rm frame}$ $\equiv$ 0 and $H_c$ = $H_f$ , the already-verified baseline; at $\omega_r$ = $\omega_0$ , exact corotation, $H_c$ = 0 and the spin’s energy in this frame vanishes identically, which is the ordinary resonance condition, not a puzzle, because $\Delta_{\rm frame}$ = - $\hbar$ $\omega_0$ $\langle$ $\sigma_z$ $\rangle$ /2 exactly cancels the lab-frame value for a state that starts, and stays,…

Equation guide → · Article →

ωr=ω0\omega_r = \omega_0ωr​=ω0​