Densara: Fermi's Golden Rule
Quantum Foundations arc, page 23 of 193. Back to The Pixelated Physics Universe
Who they are
Densara has one line, and says it often: “No final states. no transition.”
Densara is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Fermi's golden rule: transition rate Γ = (2π/ħ)|M|² ρ(Ef). With no density of final states, there is no transition.
$$ \begin{gathered} \Gamma = \frac{2\pi}{\hbar}\, |M|^{2}\, \rho(E_f) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\Gamma$ | transition rate | s^{-1} |
| $\hbar$ | reduced Planck constant | J·s |
| $M$ | transition matrix element | J |
| $\rho(E_f)$ | density of final states | J^{-1} |
Sources
- P. A. M. Dirac, Proc. R. Soc. A 114, 243 (1927)
- E. Fermi, Nuclear Physics (Univ. Chicago Press, 1950)
Crossovers
Densara meets Perturbelle (Perturbation Theory). Densara's golden rule is Perturbelle's theory carried to first order in time. The rate needs both a non-zero matrix element and a density of final states to land in.
Densara meets Broadling (Natural Linewidth). Densara sets the decay rate Γ. Broadling turns that rate into an energy width, ħ times the rate. A fast transition makes a broad spectral line.
Wear the lore
Concept keywords: Fermi's Golden Rule, Densara, Quantum Foundations, physics lore, Pixelated Physics