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It is said you can't tell one atom from another like you can't tell one electron from another, like Are atoms unique?, but:

(1) Most physics about atom system is based on Born–Oppenheimer approximation (BOA). In BOA, atomic nucleus are fixed classical source of potential and are removed from the wave functions.

The theory of identical partical origins from the behavior of wave functions when position of two particles are exchanged. This means BOA assumpts you can tell between the fixed atomic nucleus. Why does BOA work fine even it make such "wrong" assumption?

(2) Even without BOA, it is in the wave function framework that partical can't be identifid - you can't tell beween two "ideal partical" in the wave function.

Take Schrodinger's equation for a molecule without BOA as example, the "ideal particles" here are the point negative charges and the point positive charges, you really can't tell between them.

But an atom as a "sub system" of some of the "ideal particles" here, there is no such thing as "wave function's behavior when switching of two sub systems" at all, then the problem of "identify between two atoms" seems doesn't make much sense in this picture.

Since there is no strict way to say we can't tell between atoms in this picture, and telling between atoms is intuitively used almost everywhere (like two atom switch position in solid, some atom bombarded into solid, and molecule and chemical reaction), why can't we say we can tell between atoms?

Qmechanic
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jw_
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1 Answers1

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The possibility of switching between atoms does not mean that they are not identical. Even to the contrary: if they were not identical, they couldn't be switched. In my opinion, switching is better viewed as a symmetry.

The fact that the classical atoms are distinguishable is easily remedied in statistical mechanics by including $1/N!$ factor. Yet, it could be an interesting problem to treat nuclei, as if they were quantum particles. E.g., treating a hydrogen moclecule in such a way would require considering the protons on the same footing as the electrons: correctly anti-symmetrizing their spatial and spin wave function components, etc. I doubt that one would obtain new results, but it is certainly a good exercise in quantum mechanics!

Roger V.
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