#### A. Neumaier

Science Advisor

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[This thread split from https://www.physicsforums.com/threads/is-collapse-indispensable.854384/] [Broken]

ergodicity is incompatible with unitary evolution.

I don't know a reference but I can indicate a proof. Ergodicity of unitary evolution of the wave function says that for given ##\psi_0## of norm 1, ##\psi(t)=e^{-itH}\psi_0## comes for some ##t## arbitrarily close to any ##\psi## of norm 1. This is equivalent to asserting that the inner product ##\langle\psi_0|e^{itH}|\psi\rangle## gets arbitrarily close to 1. Now represent ##\psi_0## and ##\psi## in a basis where ##H## is diagonal, to verify that when ##H## is unbounded, this is for given ##\psi_0## the case only for a small minority of states ##\psi##.Could you please give a reference to this statement?

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