If I haven't understood this tricky stuff very badly when the Hamiltonian is time independent, then Schrödinger’s equation implies that the time evolution of the quantum system is unitary, but for the time-dependent Hamiltonian one must add some mathematically "put by hand" assumptions (although they make physical common sense) like causality and independence of the time evolution operator on the state of the wavefunction to ensure the time evolution operator's unitarity demanded by QM's postulates and conserve the probability density.(adsbygoogle = window.adsbygoogle || []).push({});

Even so, we still often obtain divergent series like the Dyson series, that luckily for small coupling constants get close to experiment in the first terms.

Doesn't this perentorial need of perturbation theory suggest that it would be maybe more natural either a nonlinear or a non unitary approach to time-dependent quantum theory?

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# Time evolution operator

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