Equation 131 · Part 3 · The Entry a Relabeling Cannot Write

Symbol H_f

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_f

What this part means

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

Its job in the formula

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

Full expressionSymbol H_fArticle meaning

The passage around this formula

A single case makes the term concrete and ties it to a result nearly a century old. Let $H_f$ = ( $\hbar$ $\omega_0$ /2) $\sigma_z$ , a spin precessing about a static field at its Larmor frequency, and let U(t) = $\exp(i\omega_r t\,\sigma_z/2)$ describe a frame rotating about the same axis at rate $\omega_r$ . Since U(t) is built entirely from $\sigma_z$ , it commutes with $H_f$ , so U $H_f$ $U^\dagger$ = $H_f$ …

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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 ↗

These citations provide research context; check each source for the exact claim it supports.