Proof that the probability 1 is conserved by the time evolution:
It can be derived directly from the Schrodinger equation.
- https://quantummechanics.ucsd.edu/ph130a/130_notes/node127.html from quantum physics by Jim Branson (2003).That proof also mentions that if the potential
Vis not real, then there is no conservation of probability! Therefore the potential must be real valued!
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