OK, but these effects are not due to interactions with external systems (well, maybe is not quite clear what can be considered "external"). For what I understand, the kind of interactions that can change the quantum status of a system (and make it behave as a classical system) are the ones that...
But the same is true even for an electron orbiting around an hydrogen nucleus. The presence of radiation in space does not affect the electron because the atom's energy levels that are separated by large gaps, not because of the size of the atom.
I don't see much difference between the Schrödinger equation for an electron in the field of atomic nucleus (a potential with spherical symmetry) and the Schrödinger equation for an electron in a crystal (a periodic potential). For what I understand, the fact that the crystal is a macroscopic...
Yes, I see.
My intuition would be that any system will have some spectrum of eigenvalues of the Hamiltonian.
If the spectrum is discrete, it means that the time evolution has to be the superposition of a finite set of periodic transformations. That doesn't mean that the system is periodic...
I know that is not practically achievable, but I don't think it's meaningless. Sometimes idealized experiments are very useful to understand the essential points of a physical theory.
Shrodinger's cat experiment, after all, is not considered to be meaningless, right?
As I see it, there's...
I assumed it's possible to take a "picture" of the molecule at a certain time by interacting with short wavelength photons, so that the positions of it's atoms (and then the angles between them) are determined with good accuracy
Yes, I understand.
However, I was referring to the fact that the effect of "spreading" of the values of a parameter that has a very sharp squared amplitude function is true even for bound systems: the squared amplitude of the conjugate momentum for that parameter would be a smooth function
In the Shrodinger equation for a particle in a spherical potential field in spherical coordinates, the state vector is a function of four variables: time, R, and two angles (sorry, I still didn't learn how to write formulae in this site).
For a complex molecule, the state vector would be a...
Well, for the hydrogen atom the parameters can be three real numbers: distance of the electron from the proton and two angles that determine the direction: the usual polar reference system centred on the proton. For a complex molecule made of parts that can only rotate relative to each-other...
Sorry, but I don't understand. Why the bound system should be different?
P.S. After all, any system can be considered to be bounded if you enclose it in a big-enough box, right?
I mean: in the initial state the positions are sharply determined and the velocities are spread: that's how we prepared the system. Then, since the velocities are spread, this will cause the positions to become spread too. Isn't this true?
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...