  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.
