Can Slater Determinant Explain the Difference Between Bosons and Fermions?

[hokhani]

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?

 

[Bill_K]

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.

 

[hokhani]

Thanks for replying, but According to Slater determinant when X1=X2 the antisymmetric wave function become zero.

 

[Bill_K]

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.

 

[hokhani]

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?

 

[questionpost]

If scientists have entangled more than two fermions, would that violate the principal?

 

[hokhani]

Excuse me; I was wrong
In fact the third part covers the two other parts.