Understanding the self-interaction of charged particles

Nonlinear integro-differential equations are developed in a straightforward manner which include the self-interaction of charged particles in nonrelativistic quantum mechanics. The nonlinear terms which are due to the self-interactions can be arbitrarily small for some solutions and it is argued that these are the only solutions encountered in nature. These nonlinear terms, although arbitrarily small, make the system of equations unstable and correctly account for the spontaneous emission of radiation. (author)