Fermi's Golden Rule

J. M. Zhang Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials, College of Physics and Energy, Fujian Normal University, Fuzhou 350007, China and Fujian Provincial Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Xiamen, 361005, China.

1 Deftnition

Fermi’s golden rule gives an approximate prediction of the decay rate of a discrete level imbedded in and coupled to a continuum. As a nontrivial and practical result within the first order time- dependent perturbation theory, it finds widespread use in all branches of physics. Sometimes, it appears under the guise of other names. For example, the so-called Born approximation in scattering theory is a Fermi’s golden rule result in essence.

2 History

The rule was first derived by Dirac [1, 2]. However, it was Fermi who conferred the title golden on the rule [3], possibly because of its instrumental role in his most cherished theory of Beta decay [4, 5].

3 Statement

[math]\left| b \rangle [/math]

[math]\left \langle \psi \right |[/math] [math]\left |\psi \right \langle[/math]