← Mathematical compendium

Published equation contexts

∣e,g⟩|e,g\rangle

Why this formula appears here

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 ,

Read the full article-specific guide →

Read the representative guide

ee

Symbol e

e is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →
gg

Symbol g

g is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

∣e,g⟩|e,g\rangle

Equation 81 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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 ,

Equation guide → · Article →