Do you agree that “The state of a physical system is described by a well-behaved function of the coordinates and time, Ψ(q, t). The function contains all the information that can be known about the system.”?
When the atom is coupled with the electromagnetic field and the state of the system is not separable there is no complete description of the atom given by a wavefunction defining its quantum state. You can have an incomplete description by tracing out the rest of the system, I agree.
Let’s say then that "An atom can be completely described by its quantum state only if it's isolated and in that case its energy is constant."
Edit: in any case, my point was (and I think that we will agree) that it is misleading to say “Consider a system that transitions from energy state 0 to an adjacent energy state 1. [...] To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states”.
The atom goes from the state 0 to the state 1 but during the transition it’s not described by a superposition of those states (that would be a pure state). If anything, it is described by an (improper) mixture of those states, obtained by tracing out the rest of the system.
Yes, but note that I deliberately used the word "system" rather than "atom". The system is the combination of the atom plus whatever it's absorbing energy from or emitting energy to. And that (entangled) system is in a superposition.
Ok, I was confused because if you say “Consider a system that transitions from energy state 0 to an adjacent energy state 1” it sounds as if the energy of the “system” is changing and when you say that “a particle [...] can be in two different energy states at the same time” it seems that you are referring to the atom being in a superposition of states with different energy.
One can speak meaningfully of "an atom in a superposition of energy states" despite the fact that, strictly speaking, such a thing is not possible, just as one can speak meaningfully of "the force of gravity" despite the fact that, strictly speaking, there is no such force. The latter is understood as the force-like effect of curved spacetime, and the former is understood as "an atom being a component of a system in a superposition of states with different distributions of energy" (or something like that). Communications between humans becomes more productive when we cut each other a little terminological slack.
When the atom is coupled with the electromagnetic field and the state of the system is not separable there is no complete description of the atom given by a wavefunction defining its quantum state. You can have an incomplete description by tracing out the rest of the system, I agree.
Let’s say then that "An atom can be completely described by its quantum state only if it's isolated and in that case its energy is constant."
Edit: in any case, my point was (and I think that we will agree) that it is misleading to say “Consider a system that transitions from energy state 0 to an adjacent energy state 1. [...] To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states”.
The atom goes from the state 0 to the state 1 but during the transition it’s not described by a superposition of those states (that would be a pure state). If anything, it is described by an (improper) mixture of those states, obtained by tracing out the rest of the system.