 Conservation of the square amplitude in the Schrodinger equation

ID: conservation-of-the-square-amplitude-in-the-schrodinger-equation

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Conservation of the square amplitude in the Schrodinger equation by

Ciro Santilli 37 Updated 2025-07-16

Proof that the probability 1 is conserved by the time evolution:

It can be derived directly from the Schrödinger equation.

Bibliography:

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 must be real valued!

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