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 the
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.Comment: Submitted to Physical Review D. Latex file, 8 pages. This paper is
also available at http://nucth.physics.wisc.edu/preprints
