Equation 131 · Part 1 · The Entry a Relabeling Cannot Write

Symbol H_c

H_c(t) = H_f + i\hbar\Big(i\frac{\omega_r}{2}\sigma_z\Big) = \frac{\hbar(\omega_0 - \omega_r)}{2}\sigma_z,

H_c

What this part means

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

Its job in the formula

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

Full expressionSymbol H_cArticle meaning

The passage around this formula

…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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[14] Space Quantization in a Gyrating Magnetic Field ↗

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