The Antisymmetry or Pauli Exclusion Principle

The electronic Hamiltonian in Eq. (2.10) depends only on the spatial coordinates of the electrons. To completely describe an electron it is necessary, however, to specify its spin. We do this in the context of our nonrelativistic theory by introducing two spin functions a(o ) and jS(o)), corresponding to spin up and down, respectively. These are functions of an unspecified spin variable co from the operational point of view we need only specify that the two spin functions are complete and that they are orthonormal. 

Because the Hamiltonian operator makes no reference to spin, simply making the wave function depend on spin (in the way just described) does 

This requirement, sometimes called the antisymmetry principle, is a very general statement of the familiar Pauli exclusion principle. It is an independent postulate of quantum mechanics. Thus the exact wave function not only has to satisfy the Schrodinger equation, it also must be antisymmetric in the sense of Eq. (2.22). As we shall see, the requirement of antisymmetry is easily enforced by using Slater determinants. 

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