← All parts of this equation

Equation 95 · Part 1 · The Entry a Relabeling Cannot Write

Symbol t^ast

t∗=π/(2g)t^\ast = \pi/(2g)
t∗t^\ast

What this part means

tat^ast is part of the quantity the equation computes from the expression on the right.

Its job in the formula

tat^ast is part of the quantity the equation computes from the expression on the right.

The passage around this formula

At t=0 this equals -ℏ\hbarω\omega/2 , exactly the bath’s own ground-state energy, matching the uncorrelated-bath limit derived above. At the swap time t∗t^\ast = π\pi/(2g) , the state is |g,e⟩\rangle up to an overall phase — the excitation has moved entirely into the bath — and Δ\Delta EΛ(t∗)E_\Lambda(t^\ast) = +ℏ\hbarω\omega/2 , exactly the bath’s excited-state energy with ⟨\langle HSBH_{SB}⟩\rangle = 0 at that instant, matching the closed form by direct…

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.