Equation 83 · The Entry a Relabeling Cannot Write
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol omega
omega is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
How to interpret it
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What the article says around this equation
Because conserves total excitation number, the dynamics starting from a single excitation stays confined to the two-dimensional subspace spanned by |e,g (system excited, bath in its ground state) and |g,e (the reverse). On resonance, both basis states carry the same bare energy, +/2 - /2 = 0 , so restricted to this subspace is proportional to the swap operator between the two, and the Schrödinger equation solves in closed form. Starting from | = |e,g ,
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