Equation 92 · Part 4 · The Entry a Relabeling Cannot Write

Symbol H_S

\Delta E_\Lambda(t) = \langle H_f\rangle - \langle H_S\rangle(t) = -\frac{\hbar\omega}{2}\cos(2gt).

H_S

What this part means

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

Its job in the formula

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

Full expressionSymbol H_SArticle meaning

The passage around this formula

the standard two-level exchange solution, exact for all t under this Hamiltonian. From it, $\langle$ $H_S$ $\rangle(t)$ = ( $\hbar$ $\omega$ /2)[ $\cos^2(gt)$ - $\sin^2(gt)$ ] = ( $\hbar$ $\omega$ /2) $\cos(2gt)$ , while $\langle$ $H_f$ $\rangle$ is exactly time-independent — a general fact for any state evolving under its own generator, not special to this one — and equal here to $\langle$ e,g| $H_f$ |e,g $\rangle$ = $\hbar$ $\omega$ /2 -…

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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 article section

[12] Circuit Quantum Electrodynamics ↗

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