What kind of differential equation is the Schrodinger equation?

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SUMMARY

The Schrödinger equation is classified as a parabolic differential equation, particularly for time-independent potentials, due to its formal equivalence to a diffusion equation through analytic continuation to imaginary times. The presence of the imaginary unit "i" in the equation does not hinder this classification. Mathematicians may not have a specific term to describe the complex solutions, but the parabolic nature remains a key characteristic of the equation.

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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?
 
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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.
 

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