Can Slater Determinant Explain the Difference Between Bosons and Fermions?

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Discussion Overview

The discussion revolves around the implications of the Slater determinant in explaining the differences between bosons and fermions, particularly focusing on the behavior of particles in the same position and the conditions under which they can occupy the same quantum state. The scope includes theoretical considerations and conceptual clarifications regarding wavefunctions and the Pauli exclusion principle.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that two bosons can occupy the same position, while two fermions cannot, regardless of their states.
  • Others argue that the total wavefunction must be antisymmetric, which includes position, spin, and other degrees of freedom, allowing for a spin-up fermion and a spin-down fermion to occupy the same position.
  • A participant asserts that when two fermions are at the same position, the antisymmetric wavefunction becomes zero, suggesting a strict interpretation of the Slater determinant.
  • Another participant references Wikipedia to clarify that the Slater determinant involves wavefunctions that account for both position and spin, indicating a potential misunderstanding in the original claim.
  • One participant identifies three factors that determine the Pauli exclusion principle: particles' positions, spins, and energy states, and seeks validation of this assertion.
  • A question is raised about whether entangling more than two fermions would violate the Pauli exclusion principle.
  • A later reply acknowledges a mistake regarding the third factor, suggesting it encompasses the other two factors.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the interpretation of the Slater determinant and the conditions under which fermions can occupy the same position. There is no consensus on these points.

Contextual Notes

Participants express differing interpretations of the Slater determinant and the implications for fermions and bosons, highlighting potential misunderstandings about the role of spin and position in the wavefunction. The discussion also touches on the complexity of entangled states and their relation to the Pauli exclusion principle.

hokhani
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According to Slater determinant, can one say that two bosons are able to place in the same position X , but two fermions can not, no matter what their states are?
 
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It's the total wavefunction that must be antisymmetric. This includes both the position and the spin (and any other degrees of freedom that may be present, like isospin). So for example a spin up fermion and a spin down fermion can have the same X.
 
Thanks for replying, but According to Slater determinant when X1=X2 the antisymmetric wave function become zero.
 
You're mistaken, hokhani. Since you don't believe me, take a look at the Slater Determinant page in Wikipedia. There it says, "The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital, χ(x), where x denotes the position and spin of the singular electron."

Your reference may be doing the same thing: letting the notation x stand for both spin and position combined.
 
Thanks very much
As i found out, there are 3 factors determining the pauli exclusion principal:
1) Particles' positions(x,y,z)
2) Particles' spins
3) Particles' energy states
Would you tell me if i am wrong?
 
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If scientists have entangled more than two fermions, would that violate the principal?
 
Excuse me; I was wrong
In fact the third part covers the two other parts.
 
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