Pauli observed that relativistic quantum field theory requires that particles with *half-integer* spin (s=1/2, 3/2, ...) must have *antisymmetric* wave functions and particles with *integer* spin (s=0, 1, ...) must have *symmetric* wave functions. Such observation is usually introduced as an additional postulate of quantum mechanics: *The wave function of a system of electrons must be antisymmetric with respect to interchange of any two electrons.*

As a consequence of such principle is that *two electrons with the same spin can not have the same coordinates*, since the wavefunction must satisfy the following condition:

Another consequence of the Pauli Principle is that since the ground state wave function of the He atom must also be anti-symmetric, and since the spatial part of the zeroth order wave function is symmetric, , then the spin wave function must be anti-symmetric,

(46) |

Note that this anti-symmetric spin-atom wave function can be written in the form of the