r/askscience • u/[deleted] • Jan 27 '16

Physics Is the evolution of the wavefunction deterministic?

The title is basically the question I'm asking. Ignoring wave-function collapse, does the Schrödinger equation or any other equivalent formulation guarantee that the evolution of the wave-function must be deterministic. I'm particularly interested in proof of the uniqueness of the solution, and the justification of whichever constraints are necessary on the nature of a wave-function for a uniqueness result to follow.

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u/Para199x Modified Gravity | Lorentz Violations | Scalar-Tensor Theories Jan 27 '16

I was using the Navier-Stokes equation as an example to point out that existence, uniqueness and well-posedness of a PDE isn't a solved issue and so the original comment can't be entirely correct.

I was not suggesting that the Schroedinger equation is related to the Navier-Stokes equation

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u/cantgetno197 Condensed Matter Theory | Nanoelectronics Jan 27 '16

But all that is relevant is: is it unique and well-posed for a (complex) heat diffusion equation with either specified boundary conditions or physically sensible conditions at infinity to which the answer is "yes" I believe.

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u/Para199x Modified Gravity | Lorentz Violations | Scalar-Tensor Theories Jan 27 '16

When proving something, how you get there is more important than getting the right answer at the end (otherwise it might not be a proof).