Question

Fermi's Golden Rule is particularly useful for calculating the

• A. Probability of particle decay
• B. Rate of transitions between quantum states due to a perturbation
• C. Speed of light in a vacuum
• D. Strength of the strong nuclear force

Hint:

Fermi’s Golden Rule is best remembered as a tool for computing how likely a system is to jump between energy levels when something nudges it!

Answer 1

The Correct Option is B

Fermi's Golden Rule is a key result in time-dependent perturbation theory within quantum mechanics. It provides a method to calculate the transition rate from an initial quantum state \( |i\rangle \) to a final state \( |f\rangle \) due to a weak perturbation. The rule is expressed as: \[ \Gamma_{i \to f} = \frac{2\pi}{\hbar} |\langle f | H' | i \rangle|^2 \rho(E_f) \] Here:

• \( H' \) is the perturbing Hamiltonian.
• \( \langle f | H' | i \rangle \) is the matrix element representing the coupling between states.
• \( \rho(E_f) \) is the density of final states at energy \( E_f \).

This formula is widely used in quantum optics, nuclear physics, and solid-state physics to estimate how quickly transitions occur when a system is subjected to an external influence like electromagnetic radiation.
Why other options are incorrect:

• (A) While decay can involve transitions, Fermi’s Golden Rule specifically addresses induced transitions due to perturbations, not spontaneous decay.
• (C) The speed of light in a vacuum is a fundamental constant, unrelated to perturbation theory.
• (D) The strength of the strong nuclear force is described by quantum chromodynamics, not by Fermi’s rule.