Question about the Pauli exclusion principle.

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SUMMARY

The discussion centers on the Pauli exclusion principle, which dictates that no two fermions, such as electrons, can occupy the same quantum state simultaneously. It is established that while two electrons can exist in two spin states (spin up and spin down), any attempt to create a three-electron system results in a wavefunction that vanishes due to the requirement of antisymmetry. The confusion arises from the distinction between single-particle states and the combined states of multiple particles, emphasizing that only two basis states exist for electrons, despite the potential for infinite linear combinations.

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  • Understanding of quantum mechanics principles, specifically fermions and bosons.
  • Familiarity with the concept of wavefunctions and their properties.
  • Knowledge of spin states in quantum physics, particularly for spin-1/2 particles.
  • Basic grasp of linear combinations in quantum state formulation.
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  • Study the implications of the Pauli exclusion principle in multi-electron systems.
  • Explore the mathematical formulation of antisymmetric wavefunctions for fermions.
  • Learn about the role of basis states in quantum mechanics and their significance in particle physics.
  • Investigate the concept of spin and its applications in quantum computing and quantum information theory.
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Students and professionals in physics, particularly those focusing on quantum mechanics, particle physics, and quantum computing. This discussion is beneficial for anyone seeking to deepen their understanding of the behavior of fermions and the foundational principles governing quantum states.

alemsalem
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Suppose there are only two states, and that only two electrons could fit in them (spin states for example), but wouldn't these two states form a basis and so generate an infinite number of states that are linear combinations of these two, so three electrons could be in three different states.

Obviously that's wrong, but why? do they have to be in orthogonal states?
 
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The Pauli exclusion principle arises from the requirement that the wavefunction of the system be antisymmetric under the exchange of fermionic degrees of freedom. Now you may try to write down the wavefunction with three particles, but you'll find that the antisymmetry property causes such a wavefunction to vanish.
 
alemsalem said:
Suppose there are only two states, and that only two electrons could fit in them (spin states for example), but wouldn't these two states form a basis and so generate an infinite number of states that are linear combinations of these two, so three electrons could be in three different states.

Obviously that's wrong, but why? do they have to be in orthogonal states?


I think there is some confusion here. There are two states, yes, so in principle, you can form an infinite number of states through linear combinations, but those are one particle states.

For a two particle state, the only one allowed is the state where one particle is spin up and the other is spin down. There is only one state for for the combined system.

I hope that helps.
 
Should i forward a conclusion that linear combination of the spin functions of the electron cannot be done: that means ultimately there are only 2 possible spin states for an electron ! Anyone can further comment this ?
 
gerrardz said:
Should i forward a conclusion that linear combination of the spin functions of the electron cannot be done: that means ultimately there are only 2 possible spin states for an electron ! Anyone can further comment this ?

There are only two possible BASIS states for the spin states for an electron since they are spin 1/2. However, there an infinite number of spin states for an electron because you can make any number of other states by performing a linear combination of these 2 states.

I hope I got your question correct.
 

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