Multipole expansions in quantum radiation theory

Abstract: With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation amplitude in the form of the sum of radiation amplitudes of electric and magnetis multipole photons. All information about the radiating system is contained in the coefficients of the series which are the irreducible tensors being determined by the current density of transition. The expansion can be used for solving different problems that arise in studying electromagnetic field-quantum system interaction both in long-wave approximation and outside its framework.