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?
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.
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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