Fermi Golden Rule Calculator

Calculate quantum transition rates and decay lifetimes

Transition Type:

Matrix Element |V| (eV):

Density of States ρ(E) (states/J):

About Fermi's Golden Rule

Fermi's Golden Rule gives the transition rate from an initial quantum state to a continuum of final states under a weak perturbation. It is fundamental to understanding decay processes and scattering.

The Golden Rule:

Γ = (2π/ℏ)|⟨f|V|i⟩|² ρ(Ef)
V = perturbation Hamiltonian
ρ(E) = density of final states
τ = ℏ/Γ = lifetime

Applications:

Spontaneous emission of photons
Nuclear decay processes
Scattering cross sections
Electron-phonon interactions

💡

Help us improve!

How would you rate the Fermi Golden Rule Calculator?