The electromagnetic field term

This last expression is known as Fermi s golden rule. For transitions from one single-particle state to another single-particle state in which case neither the density of states g(e/) nor the dependence of the transition probability on c/ enter, the transition rate takes the form 

An example of the application of perturbation theory is the motion of a particle of mass m and charge in an external electromagnetic field. The electric field, E, is given in terms of the scalar and vector potentials 1 , A as 

We will adopt this expression as the quantum mechanical hamiltonian of the particle, by analogy to that for the free particle. Moreover, we can choose the vector and scalar potentials of the electromagnetic fields such that V, A = 0, I — 0, a choice called the Coulomb gauge (see Appendix A). 

Our goal now is to determine the interaction part of the hamiltonian, that is, the part that describes the interaction of the charged particle with the external electromagnetic field, assuming that the latter is a small perturbation in the motion of the free particle. We will also specialize the discussion to electrons, in which case m = Me,q = —e. In the Coulomb gauge, we express the vector potential as 

Quantum Mechanics, L.I. Schiff (McGraw-Hill, New York, 1968). 

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In 1917, Albert Einstein discovered the fundamental principal by which light can interact with matter to amplily the intensity of the electromagnetic field, termed stimulated emission. Indeed, the word laser is an acronym for light amplification by the stimulated emission of radiation. 

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