I have questions: you describe the change of states of particle as
"a smooth transition between being in one energy state to
being in a superposition of two energy states to being
entirely in the second energy state."
At the terminus of this transition, is the particle no longer in a superposition? IE there is now a 100% chance it's in the second state and 0% chance that it's in the original state?
If so, does that imply that the function of the particle's state (with respect to time) is discontinuous? Since there's a point at which it goes from being a superposition to exactly 0%.
The first answer is that a system is never 100% in any particular state because that would violate the uncertainty principle. When we speak of a system "definitely" being in a particular state that's an approximation/simplification. It actually means that the system is in a superposition of some range of states that for all intents and purposes we can treat as being the same, and the probability of it being in a state that cannot be treated the same for all intents and purposes is so close to zero we can ignore that.
The second answer is that whether or not a system is in a superposition depends on your point of view. A system can only ever be in a "single state" (according to the above approximation) with respect to some observable, and if it is in a single state with respect to that observable then it is necessarily in a superposition with respect to the complementary observable, e.g. a particle that is in a definite state with respect to position is necessarily in a superposition with respect to velocity.
So the whole process is everywhere and always continuous.
If so, does that imply that the function of the particle's state (with respect to time) is discontinuous? Since there's a point at which it goes from being a superposition to exactly 0%.