2-Fermion Systems

In order to get a feeling for how to work with Fermion systems, we start with the simplest case $N=2$. The basis states are the Slater determinants

$$\langle \xi_1,\xi_2 \vert\nu_1,\nu_2\rangle_A = \frac{1}{\sqrt{2!}} \left\vert \begin{array}{cc} \psi_{\nu_1}... ...nu_2}( \xi_1) & \psi_{\nu_2}( \xi_2) \\ \end{array}\right\vert$$

$$= \frac{1}{\sqrt{2}}\left[ \psi_{\nu_1}( \xi_1)\psi_{\nu_2}( \xi_2) - \psi_{\nu_1}( \xi_2)\psi_{\nu_2}( \xi_1) \right].$$ (2.1)