- #26

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No, by "coherent superposition" I meant a pure state, as opposed to a mixed state.Are you talking aboutexactcoherent states, involving an infinite (and not finite) number of photons?

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- #26

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No, by "coherent superposition" I meant a pure state, as opposed to a mixed state.Are you talking aboutexactcoherent states, involving an infinite (and not finite) number of photons?

- #27

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I don't think that it is how we usually define a quantum system, although I admit that some pragmatic physicists do prefer to define quantum systems in that way.Usually we define a quantum system by its interaction with a classical surrounding.

Nothing, of course.What is the classical surrounding of the whole universe?

- #28

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H-atom in an excited state is an energy eigenstate of the free-atom Hamiltonian. However, it is not an energy eigenstate of the total Hamiltonian including the interaction with quantum electromagnetic field. This is why this system is unstable.Consider an isolated H-atom in an excited state (for example 2p).

This is an energy eigenstate and stationary.

However, we know that the H-atom can emit a photon and go to the ground state. The total energy of the system does not change.

- #29

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So where (or when) do we need to discuss collapse, if not here? And can collapse ever transform an eigenstate of Hamiltonian into a non-eigenstate of Hamiltonian?Incorrect. Hamiltonian of the closed universe includes all the measurements in said universe. That means if you are in an eigen state of Hamiltonian, the measurement won't change that either. It's only when you are considering sub-systems that distinction is relevant.

The only way you can have dynamics in the universe is if universe is not in an eigen state of the Hamiltonian. And why should it be in an eigen state? There are infinitely more states than there are eigen states.

So we don't need to discuss collapse here. The universe is in some super-position of eigen states, and that's enough.

- #30

K^2

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If you are talking about pure vs mixed states, that is exactly how you are defining your system. The distinction is only relevant statistically, and that implies an external system.I don't think that it is how we usually define a quantum system, although I admit that some pragmatic physicists do prefer to define quantum systems in that way.

Excited atom + ground state EM vacuum is still an eigen state of such a system.H-atom in an excited state is an energy eigenstate of the free-atom Hamiltonian. However, it is not an energy eigenstate of the total Hamiltonian including the interaction with quantum electromagnetic field. This is why this system is unstable.

But stability is a separate issue. 2p is unstable even in basic Hydrogen atom Hamiltonian. 2p + ε 1s already has dipole moment and will radiate. So a small perturbation will result in decay. That's the definition of instability.

- #31

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DrDu was talking about a CLASSICAL surrounding, while what you say above refers to a QUANTUM surrounding.If you are talking about pure vs mixed states, that is exactly how you are defining your system. The distinction is only relevant statistically, and that implies an external system.

It would be so if there was no interaction term in the Hamiltonian describing atom and EM field. But the interaction term is there, so what you say above is not correct.Excited atom + ground state EM vacuum is still an eigen state of such a system.

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