Exact solutions for matter-enhanced neutrino oscillations

The analogy between supersymmetric quantum mechanics and matter-enhanced neutrino oscillations is exploited to obtain exact solutions for a class of electron density profiles. This integrability condition is analogous to shape invariance in supersymmetric quantum mechanics. This method seems to be the most direct way to obtain the exact survival probabilities for a number of density profiles of interest, such as linear and exponential density profiles. The resulting neutrino amplitudes can also be utilized as comparison amplitudes for the uniform semiclassical treatment of neutrino propagation in arbitrary electron density profiles.