Why is a time-dependent Hamiltonian different 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. 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.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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