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Equation 85 · Part 1 · The Entry a Relabeling Cannot Write

Symbol psi

∣ψ(0)⟩=∣e,g⟩|\psi(0)\rangle = |e,g\rangle
ψ\psi

What this part means

psi is part of the quantity the equation computes from the expression on the right.

Its job in the formula

psi is part of the quantity the equation computes from the expression on the right.

The passage around this formula

Because HSBH_{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, +ℏ\hbarω\omega/2 - ℏ\hbarω\omega/2 = 0 , so HfH_f restricted to this subspace is proportional to the swap operator between the two, and the Schrödinger equation solves in closed form. Starting from |ψ(0)\psi(0)⟩\rangle = |e,g⟩\rangle ,

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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