Equation 85 · Part 4 · The Entry a Relabeling Cannot Write

=

|\psi(0)\rangle = |e,g\rangle

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article 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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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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.