I would like to know how to derive the wave function of two non-intering electrons in one-dimensional space by accounting their spin and Pauli's exclusion principle.
$\Psi(x_1, x_2,\sigma_1, \sigma_2)$ and $V(x_1, x_2) = V(x_1) + V(x_2)$
I'm just wondering that if I can use the form of separable wavefunction
$\Psi(x_1, x_2,\sigma_1, \sigma_2) = \psi(x_1, x_2) \cdot \chi(\sigma_1, \sigma_2) = \psi_1(x_1)\psi_2(x_2) \cdot \chi_1(\sigma_1)\chi_2(\sigma_2)$
Subtituting it in Schrodinger equation would yeild the same result as the case without spin.