Energy conservation in approximated solutions of multiple beam scattering problems

TL;DR

This paper demonstrates that series expansion solutions like the Born approximation can violate energy conservation in multiple beam scattering problems, and outlines conditions for consistent solutions.

Contribution

It reveals energy violation issues in common approximation methods for multiple beam scattering and proposes basic conditions for consistent solutions.

Findings

Series expansion solutions can lead to energy violation.

Conditions for energy-conserving solutions are outlined.

Implications for quantum scattering analysis.

Abstract

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.