Pauli Exclusion Principle

hokhani · Feb 18, 2012

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 · Feb 18, 2012

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 · Feb 18, 2012

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

Bill_K · Feb 19, 2012

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 · Feb 19, 2012

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 · Feb 19, 2012

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

hokhani · Feb 20, 2012

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