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\bgroup\color{col1}$ N$\egroup-particle system

We have \bgroup\color{col1}$ N$\egroup particles and \bgroup\color{col1}$ N$\egroup quantum numbers \bgroup\color{col1}$ \nu_1$\egroup,..., \bgroup\color{col1}$ \nu_N$\egroup. A basis consists of all product states \bgroup\color{col1}$ \vert\nu_1,...,\nu_N\rangle$\egroup corresponding to wave functions \bgroup\color{col1}$ \psi_{\nu_1}( \xi_1)...
\psi_{\nu_N}( \xi_N)$\egroup, \bgroup\color{col1}$ \xi={\bf r}\sigma$\egroup,
$\displaystyle \vert\nu_1,...,\nu_N\rangle \leftrightarrow \psi_{\nu_1}( \xi_1)....
...\nu_N}(\xi_N)=\langle \xi_1\vert\nu_1\rangle ...\langle \xi_N\vert\nu_N\rangle.$     (1.6)

These wave functions still don't have any particular symmetry with respect to permutation of particles. We use them to construct the basis wave functions for Bosons and Fermions.



Tobias Brandes 2005-04-26