I've seen it stated in many places that the reason why atoms don't collapse is due to the pauli exclusion principle. The exclusion principle is given as a required anti-symmetry in the wavefunction of electrons.(adsbygoogle = window.adsbygoogle || []).push({});

I don't understand how this principle was derived, or where it comes from. (I've seen the derivaiton in Bates, but all that proves is that wavefunctions that start either symmetric or asymmetric, that have a Hamiltonian that is symmetric with respect to particles (particles behave the same) will remain symmetric or antisymmetric.)

It seems to me that the electrostatic repulsion of electrons suffices to explain the electronic structure of an atom. If you have a joint wave-function for 2 electrons, the electrostatic repulsion potential would enforce Phi(x,x) = 0 for states where x1=x2. If you had "boson electrons" where Phi(x2,x1) = +Phi(x1,x2), but Phi(x1,x1) = 0 due to the electrostatic repulsion, how you could distinguish between the behavior of an atom with "boson electrons" and one with "fermion electrons"? The conjugate product of the wavefunction with itself should come out the same in both cases.

If you cannot distingish between these cases, then why is antisymmetry necessary to explain electronic structure, and not simply some sort of repulsion potential that blows up at 0 distance? (The repulsion potential ensures that the ground state wavefunction cannot be separable, and isn't equivalent to the independent ground state wavefunctions of single electrons in the same potential)

What experiment could you build that could distinguish between particle symmetry vs. antisymmetry that isn't also confounded with fermions all having repulsion interactions in terms of other forces?

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# Pauli exclusion principle question (again)

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