In preparation for future work on the effects of a strong magnetic field in white dwarf of neutron stars we calculated the Thomson scattering in a fully ionized collisionless high density plasma. Quantum mechanical perturbation theory and the density matrix are used to compute the Stokes parameters for the scattered radiation in terms of the polarization state of the incident wave, the electron-cyclotron frequency, the angle of incidence, and the angle of scattering. Various regimes of density and magnetic field strength are studied in detail for possible applications to late stage stellar evolution. The criterion for the magnetic field to substantially affect the Stokes parameters is that the photon frequency be less than the electron-cyclotron frequency.
