What kind of differential equation is the Schrodinger equation?

[AxiomOfChoice]

Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?

 

[Mute]

At least for time-independent potentials, the Schrödinger equation is formally equivalent to a diffusion equation (parabolic) via analytic continuation to imaginary times, so in that sense one could call it parabolic, but I'm not sure if Mathematicians have a reserved term to account for the fact that the solutions are complex numbers.