Electron spin transition solution applicable to an ensemble of isolated electrons.

An electron spin aligned with a static magnetic field changes its orientation when subjected to a time-varying magnetic field which is directed perpendicular to the static magnetic field. This well-known phenomenon is readily calculated when the time-varying magnetic field is circularly polarized; however, the evolution of the spin-state wavefunctions becomes much more difficult to calculate when the time-varying magnetic field is linearly polarized. For linear polarization and isolated spins, an analytic solution has been derived for the dynamical spin-state wavefunctions. Part of the solution procedure relies on an expansion using a small parameter, which is the ratio of the amplitude of the time-varying magnetic field to the static magnetic field. To verify the validity of the expansion technique, a numerical solution of the basic equations is compared to the analytic solution. Results are found to agree to better than 10% for exact resonance and better than 5% in general.