# Identical fermions in the same quantum state

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?

-
Have you thought that a hydrogen atom is not a fermion? It has an equal number of protons and electrons so the minimum spin is 0, and it is a boson anyway. An unlimited number of bosons can fit in the same energy level/state. They are indistinguishable. Two hydrogen atoms one meter apart will be meeting different potentials and energy levels anyway. Meters are in the realm of classical physics. – anna v Mar 30 '13 at 16:19
I did not think of the hydrogen as a boson! I guess my question would be if I picked an element that is a fermion, say Lithium atoms? – QEntanglement Mar 30 '13 at 16:29
Because atoms are neutra, i.e. equal numbers of electrons and protons, they all are bosons. An ion, an electron missing, becomes a fermion. – anna v Mar 30 '13 at 16:46
Okay, say I have two ions then. Can their remaining electrons be in the same orbital, same energy state, and same spin state? Can this happen if the two ions are separated by a large distance? – QEntanglement Mar 31 '13 at 2:26
Did you not see Lubos' answer? The first paragraph covers these changed conditions. As long as there is a different (x,y,z) coordinate the eigen states are different.( BTW an odd number of baryons would also make an atom have at least spin 1/2) – anna v Mar 31 '13 at 4:32