- Clarification on Pauli exclusion princple.
The exlcusion principle seems intuitive enough to me when the states being considered are eigenstates, however how does it work exactly with general states? It seems to me that if we're allowed to consider general quantum states then the principle breaks down, since we can always find states that are only infinitesimally distinct. For example if we had ##N## free fermions, couldn't we have them all in the same exact momentum state but simply with infinitesimally small but distinct contributions from other states? I ask this because I do not entirely understand why electrons in atomic orbits are always assumed to be in energy eigenstates and hence strongly affected by the exclusion principle, couldn't we have all the electrons in an atom in the ground state but each with a different superposition of spin up and down?