Spontaneous emission according to quantum

The quantized field theory of radiation treats the radiation field as an ensemble of harmonic oscillators, each mode of the field being associated with an oscillator of angular frequency w and having the allowed energies  

The theory now treats the combination of an atom plus the radiation field as a single system. If the system is in an initial state in which there are n, quanta in the 

This is independent of the vectors k and because an average has been performed over the directions of k and e corres- 

It is therefore plausible to suppose that they are also responsible for spontaneous emission. 

An alternative explanation of the mechanism of spontaneous emission has been proposed by Wheeler and Feynman (1945) in a theory which includes both the retarded and advanced electromagnetic potentials introduced in section 2.6. The difference between the two theories is most evident if we consider a hypothetical universe containing a single 

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