Equation 76 · Part 6 · The Entry a Relabeling Cannot Write

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H_S = (\hbar\omega/2)\sigma_z^S

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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

A single exactly solvable case makes the ledger’s behavior concrete, and it is worth being explicit that what follows is an analytic evaluation of a stated model, not a simulation and not a measurement. Let S and B each be a two-level system — a spin, in the sense this literature uses the word for any two-state quantum degree of freedom — with bare Hamiltonians $H_S$ = ( $\hbar$ $\omega$ /2) $\sigma_z^S$ and $H_B$ = ( $\hbar$ $\omega$ /2) $\sigma_z^B$ tuned to the same frequency $\omega$ , coupled by an excitation-conserving exchange term,

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

[12] Circuit Quantum Electrodynamics ↗

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