Fermions, Pauli and antisymmetry

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SUMMARY

Pauli's exclusion principle, which states that no two fermions can occupy the same quantum state, is fundamentally rooted in the antisymmetry of their wave functions. This principle is derived from quantum field theory (QFT) and is considered an axiom in quantum mechanics (QM). Pauli's insights into electron shell filling and the spin statistics theorem, as published in his 1940 papers, further elucidate the behavior of fermions. The antisymmetry of fermions is a unique characteristic of quantum theory, with no classical analog.

PREREQUISITES
  • Understanding of quantum mechanics (QM) principles
  • Familiarity with quantum field theory (QFT)
  • Knowledge of wave function behavior in quantum systems
  • Basic concepts of fermions and bosons
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  • Research the derivation of the antisymmetry condition for identical fermions in quantum field theory
  • Study Pauli's spin statistics theorem and its implications for particle physics
  • Explore the historical context of Pauli's exclusion principle and its impact on atomic theory
  • Investigate the mathematical formulation of wave functions for fermions and their applications
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Physicists, students of quantum mechanics, and researchers in particle physics will benefit from this discussion, particularly those interested in the foundational principles governing fermionic behavior and the historical development of quantum theory.

imsmooth
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How did Pauli determine his exclusion principle? Was it based on how he posited electron shells filled? Is the fact that fermions are antisymmetic a mathematical solution to make the principle work with quantum theory?
 
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imsmooth said:
How did Pauli determine his exclusion principle? Was it based on how he posited electron shells filled? Is the fact that fermions are antisymmetic a mathematical solution to make the principle work with quantum theory?
I don't know the historical side, but I think it became clear that there must be some principle at work to prevent all electrons reaching the ground state.

That the wave function for identical fermions must be totally antisymmetric can be derived from QFT. As far as straight QM goes, it's essentially an axiom.

There is nothing like it outside of quantum theory: it's a purely QM phenomenon.
 
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I think it was also Pauli who derived a first version of the spin statistics theorem.
 
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