If we are to take two Hydrogen atoms and subject them to the same potential, then wouldn't both Hydrogen atoms be in the same exact quantum state? This bother me because no two identical fermions can be in the same quantum state! This seems to contradict the principle. This applies to any two elements or molecules that are subjected to the same potential.
Say these two Hydrogen atoms are located 1m from each other, then would the only way to distinguish them would be their spatial location?
What is the technical term for two seemingly identical things to be distinguishable by their location?