What kind of differential equation is the Schrodinger equation?

  • #1
AxiomOfChoice
533
1
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?
 

Answers and Replies

  • #2
Mute
Homework Helper
1,388
12
At least for time-independent potentials, the Schrodinger 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.
 

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