Source: cirosantilli/conservation-of-the-square-amplitude-in-the-schrodinger-equation
= Conservation of the square amplitude in the Schrodinger equation
Proof that the probability 1 is conserved by the time evolution:
It can be derived directly from the <Schrödinger equation>.
Bibliography:
* https://quantummechanics.ucsd.edu/ph130a/130_notes/node127.html from <quantum physics by Jim Branson (2003)>.
That proof also mentions that if the potential `V` is not real, then there is no conservation of probability! Therefore the potential \i[must] be real valued!