I was trying to answer a very simple question: how does QM resolve the classical physics paradox of the electrons falling inside the atomic nucleus by emitting EM-radiation.
Well, in short, the answer is that atoms generally occupy a well defined energy state. If you assume this and use the schrödinger equation, you will have a discrete set of solutions, none of which exist inside the nucleus.
However, these solutions are not all of the possible physical states the electron could be in. You could have a superposition of energy levels and using these you could get the electron to be anywhere you really want. Then again, using the time evolution part of the schrödinger equation you would see that only the well defined energy level electrons wouldn't be evolving in time. But why is this a problem? Why can't the electron be evolving in time?
To this question I reasoned that the interaction between the atoms and the environment is the cause and that in pricipal a completely isolated atom could exist in a energy superposition indefinitely. But then again is this a good reason? Why do interactions between the environment force the wavefunction to adopt energy eigenstates and not, for example, position or momentum*?
*I do know that pure eigenstates of for example momentum are not physically possible but states which have a tiny standard deviation around some value certainly are.
