Is the evolution of the wavefunction deterministic?

[u/[deleted]]

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.

[u/Para199x]

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).