Exact solutions of Dirac equation on a 2D gravitational background
  We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified supersymmetric harmonic oscillator the wave function and energy spectrum of Dirac equation is given explicitly. 
S. K. Moayedi, F. Darabi