Particle in superposition of energy eigenstates and conservation of energy.

[Demystifier]

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.

DrDu was talking about a CLASSICAL surrounding, while what you say above refers to a QUANTUM surrounding.

Excited atom + ground state EM vacuum is still an eigen state of such a 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.

 

[Time_]

The notion of a closed universe is quite interesting. Demystifier to expand on what you are saying, if energy eigenstates, so the different superpositions of a particle, must evolve into a coherent state, where does all this excess energy from these states go? Our universe,in accordance with things such as Pauli Exclusion can only have on outcome of a solution, and the physical existence of a particle in two different states seems impossible. Could it be that many worlds theory holds valid in that all these different energy eigenstates come together to form an infinite number of possibly universes, each branching from another, as a wave function collapses and the other superpositions become irrelevant to our world?