  Solutions in the form of series expansion, as the Born approximation, are
very useful for describing time-independent scattering of quantum particles. In
this work, it is mathematically demonstred that such solutions, when applied to
multiple beam scattering phenomena, can lead to energy violation where the
number of incident and scattered particles is not preserved. General basic
conditions for developing consistent solutions of time-dependent multiple beam
scattering problems are outlined.

Materials Science