Time-dependent Schr\"odinger equations having isomorphic symmetry   algebras. I. Classes of interrelated equations
  In this paper, we focus on a general class of Schr\"odinger equations that are time-dependent and quadratic in X and P. We transform Schr\"odinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ``time'' variable. We derive mathematical constraints forthe transformation and introduce two examples. 
Michael Martin Nieto and D. Rodney Truax