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Conservation of the square amplitude in the Schrodinger equation

Ciro Santilli (@cirosantilli, 37) ... Physics Particle physics Quantum mechanics Non-relativistic quantum mechanics Schrödinger equation Conservation laws in Schrodinger equations
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
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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    • Probability current Conservation of the square amplitude in the Schrodinger equation

Probability current

 1  0
Conservation of the square amplitude in the Schrodinger equation

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