The Fermi Golden Rule is a fundamental formula in quantum mechanics. It calculates the rate at which a quantum system transitions from an initial state to final states due to a weak perturbation. This rule is essential for understanding many quantum processes in physics.
The Fermi Golden Rule is expressed mathematically as gamma equals two pi over h-bar times the absolute square of the matrix element times the density of final states. The matrix element represents the strength of the perturbation coupling, while the density of states accounts for how many final states are available at the transition energy.
The Fermi Golden Rule works through a specific physical mechanism. First, a weak perturbation disturbs the quantum system, providing the energy needed for transitions. Second, energy conservation ensures transitions only occur between states with matching energies. Finally, for sufficiently long times, the transition rate becomes constant and time-independent.
The Fermi Golden Rule has numerous applications across physics. It calculates atomic transition rates for photon absorption and emission. It determines radioactive decay rates of unstable nuclei. It predicts scattering cross-sections in particle interactions. And it describes electron transitions in condensed matter systems and quantum devices.
To summarize what we have learned: The Fermi Golden Rule is a fundamental quantum mechanical formula that calculates transition rates between quantum states. It depends on both the strength of the perturbation and the availability of final states. This rule is essential for understanding many physical processes from atomic physics to nuclear decay, making it one of the most important tools in quantum mechanics.