Wave function of two different fermions

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SUMMARY

The wave function of two different fermions must be antisymmetric according to quantum field theory principles. When constructing the state of two identical fermions using the creation operators b^\dagger(p_1) and b^\dagger(p_2), the antisymmetry arises from the anticommutation relation \{b^\dagger(p_1), b^\dagger(p_2)\} = 0. For two different fermions, represented by b^\dagger(p_1) and d^\dagger(p_2), the same anticommutation relation holds, confirming that the wave function remains antisymmetric. Thus, the Pauli exclusion principle applies only to identical fermions, and different fermions do not require antisymmetry in their wave functions.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with fermionic creation operators
  • Knowledge of antisymmetry in wave functions
  • Basic grasp of the Pauli exclusion principle
NEXT STEPS
  • Study the implications of the Pauli exclusion principle in quantum mechanics
  • Learn about the properties of fermionic wave functions
  • Explore the role of anticommutation relations in quantum field theory
  • Investigate the differences between identical and non-identical particles in quantum systems
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Physicists, quantum mechanics students, and researchers in quantum field theory who are exploring the behavior of fermions and the implications of particle identity on wave functions.

Marchigno
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Hi! According to quantum field theory, must the wave function of two different fermions be antisymmetric?
If I have a state of two equal fermions: [tex]b^\dagger(p_1)b^\dagger(p_2)|0>[/tex] I can construct the general state of two fermions:
[tex]\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)b^\dagger(p_2)|0>[/tex]
where f is the wave function. Now because [tex]\{b^\dagger(p_1),b^\dagger(p_2)\}=0[/tex]
the wave function f mast be antisymmetric.
The question is: if I now consider two different fermions: [tex]b^\dagger(p_1)d^\dagger(p_1)|0>[/tex]
so that the general state is
[tex]\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)d^\dagger(p_2)|0>[/tex]
because
[tex]\{b^\dagger(p_1),d^\dagger(p_2)\}=0[/tex]
remains true, does it mean the wave function of any two fermions will be antisymmetric? I thought it was true only for two identical particles!
Thank you for the answers! :)
 
Physics news on Phys.org
If the fermion are not identical, then there is no possible symmetry to start with, so the Pauli principle does not apply.
 

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