Why is a time-dependent Hamiltonian different in quantum mechanics?

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SUMMARY

The discussion centers on the distinction between time-dependent Hamiltonians in classical mechanics and quantum mechanics. In classical mechanics, an explicit time dependence in the Hamiltonian indicates that it does not represent the total energy of the system, while in quantum mechanics, this relationship can differ due to the nature of quantum states and operators. The participants express confusion regarding the implications of external potentials on the Hamiltonian's time dependence and seek clarification through examples, highlighting the complexity of quantum systems.

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In classical mechanics, if there's an explicit time dependence in the Hamiltonian of a system, then it won't be equal to the system's total energy. Why isn't this true in quantum mechanics?
 
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In classical mechanics, if there's an explicit time dependence in the Hamiltonian of a system, then it won't be equal to the system's total energy.
Can you show an example of this?

If the time-dependence in the Hamiltonian is just some external potential, it should be fine. And I do not see how you get different time-dependent expressions in quantum mechanics - the particles and fundamental interactions have to stay the same.
 
mfb said:
Can you show an example of this?

No, I can't. I just confused myself. Thanks.
 

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