Light scattering on exciton resonance in a semiconductor quantum dot: Exact solution

We find an exact solution to the problem of light scattering on exciton resonance in a semiconductor quantum dot surrounded by a medium with a given dielectric constant. This enables us to obtain the exciton resonant-frequency renormalization due to the long-range electron-hole exchange interaction and exciton radiative lifetime to any order in the ratio of the quantum dot size to the wavelength of light. We find spatial distribution of the electric field both inside and outside the quantum dot.