Families of exact solutions of a 2D gravity model minimally coupled to   electrodynamics
  Three families of exact solutions for 2-dimensional gravity minimally coupled to electrodynamics are obtained in the context of ${\cal R}=T$ theory. It is shown, by supersymmetric formalism of quantum mechanics, that the quantum dynamics of a neutral bosonic particle on static backgrounds with both varying curvature and electric field is exactly solvable. 
S. K. Moayedi, F. Darabi