Equation 84 · Part 2 · The Entry a Relabeling Cannot Write

subscript

H_f

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

Because $H_{SB}$ conserves total excitation number, the dynamics starting from a single excitation stays confined to the two-dimensional subspace spanned by |e,g $\rangle$ (system excited, bath in its ground state) and |g,e $\rangle$ (the reverse). On resonance, both basis states carry the same bare energy, + $\hbar$ $\omega$ /2 - $\hbar$ $\omega$ /2 = 0 , so $H_f$ restricted to this subspace is proportional to the swap operator between the two, and the Schrödinger equation solves in closed form. Starting from | $\psi(0)$ $\rangle$ = |e,g $\rangle$ ,

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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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