Abstract
We consider source–neutral problems for periodic problems in electrostatics. These may be used to derive an identity due to Lord Rayleigh entirely within the context of the unit cell, and without use of reasoning based on contributions from charges at an outer boundary of the periodic system, or employing conditionally convergent lattice sums. We also consider the equivalent of source–free Green9functions for the Helmholtz equation, which are Green9functions with their specular parts removed. We show that, as the wavenumber tends to zero, the non–specular dynamic Green9functions tend with no divergences to the source–neutral electrostatic Green9function.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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