Main Question or Discussion Point
Can one deduce from Pauli's exclusion principle (through the Slater Determinant) that two electrons with different spins in the same energy level, can't have the same position?
It says, "No two electrons in a system can be in the same one-particle state... Note that in the statement “one-particle state” refers to both space and spin parts."
I haven't got any answer to the question above. Could anyone please answer the question?Let me explain my problem clearly. In the expression [itex]\psi _\alpha (x)[/itex] for wave function of an electron, [itex]\alpha[/itex] is the state and [itex]x[/itex] includes both position and spin. I don't know whether [itex]\alpha[/itex] includes the spin or not and if it includes spin, is this spin the spin existed in the [itex]x[/itex]?
It works like this: In reality, there is no wave function for an electron. There is only a single wave function for the N-electron system. In the Hartree-Fock approximation, this is a single Slater determinant Θ (and in the general case, it can be written as a linear combination of Slater determinants).I haven't got any answer to the question above. Could anyone please answer the question?