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Simplest fermionic normalized quantum many-particle wavefunction in position representation

displaystyle\Psi(z_1,z_2,\ldots,z_N)=\big(4\pi(N-1)\big)^{-N(N-1)/2}\prod_{i<j}^N(z_i-z_j)e^{-\frac{1}{4}\sum_{i=1}^N|z_i|^2}\ ,$ in terms of complex coordinates $z=x+iy$ and with physical constants set to 1 (normalization
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