PeroK said:
I think you need to be more specific about what you're asking. A molecule isn't a macroscopic system - and, in any case, may be in an eigenstate of the Hamiltonian and stable indefinitely.
In QM the position of a free particle becomes more spread out over time, which seemed to be the basis of your original analysis. That doesn't mean that the constituent particles in a molecule naturally drift apart.
Well, I was trying to understand how is it possible to reconcile the fact that the system's status becomes more and more spread out over the time with the fact that the unitary evolution is really periodic. So, it should return to the non-spread status periodically. This seems to me somehow contradictory.
If the system is a set of free particles, then it's easy to understand that the positions become spread over all available space and will never return to the initial position in a reasonable amount of time.
But what if I have a system that has a lot of degrees of freedom (let's say 10 real variables that describe some angular positions, to fix the idea - plus related momentums), but it's not made of free particles?
The system that I have in mind, for example, is this: take a molecule with a complex structure (for example a protein), that at a certain temperature can move only with 10 degrees of freedom - that are angles between various triplets of atoms: so there will be some rigid parts of the molecule that don't move and some that can rotate relatively to each-other. The position of the molecule is not important, we can consider it fixed in space.
To make the experiment, let's say that we "take a picture" of the position of the status with a fast flash of light able to determine our 10 parameters with some small indeterminacy, leaving the 10 momentums with much more indeterminacy.
Then, the isolated system will start to evolve in time, and our 10 position parameters will start to spread, since there is a lot of indeterminacy in the 10 momentums.
But then what will happen to evolution of the 10 position parameters? will they remain spread forever, or will they return to the original status of determined position and spread momentums?
If the evolution in time is periodic, probably there will be a discrete (even if very big) set of eigenvalues of energy, and the status of the system can even be described as a superposition of probability amplitudes of the energy eigenstates.
So, in the end the thing that I would like to understand is: is it possible to describe any finite system in this way, however big, treating it basically as a superposition oscillators with relative amplitudes, or is there something fundamentally different in systems that are "big enough"?
Well, sorry for the very long explanation :-)