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You basically have three questions: as people always say: Schrödinger picture does not include time-dependent operators. They mean operators like momentum, position, etc not depend on time, not the Hamiltonian. I am not so sure whether this operator should satisfy.... Yes, they satisfy the relation, so does the Hamiltonian. However because the ...


First of all, let me say the following: If anyone (perhaps you, @V.Moretti?) would be able to provide a more mathematically oriented perspective on this question, I think that would make a valuable complement to this answer, which can be characterized as pragmatic (or handwavey, depending who you'd ask!), rather than deep. That being said, I will now answer ...

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