# Pauli Exclusion Principle

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.

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.

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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