Operator Transformations Between Exactly Solvable Potentials and Their   Lie Group Generators
  One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also, potentials related by real transformation functions are shown to have the same spectrum generating algebra with Hermitian generators related by this operator transformation. 
Andrew J. Bordner