Approximate solution of the Lee model in all sectors

The Pauli–Källén equation for unstable particles is reduced to a canonical equation. This is solved approximately. The method of solution is illustrated on the Pauli–Källén equation in the $V-\theta$- and $V-2\theta$ sectors and is generalized to arbitrarily many $\theta$ particles. The method enables one to carry through the treatment for stable particles as well. The solutions that are obtained can be used to describe the energy, angular, and polarization distributions of stimulated radiation and to investigate the stimulated decay of unstable particles.