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I'm trying to calculate two-electron Slater determinant for orbitals $\Psi_1(r, \sigma)=\varphi(r) \alpha (\sigma)$ and $\Psi_2(r, \sigma)=\varphi_1(r) \beta (\sigma)$. Is the determinant supposed to be written like this?

$\Psi=\frac{1}{\sqrt{2}}$ $\begin{vmatrix} \varphi(r) \alpha (\sigma) & 0 \\ 0& \varphi(r) \beta (\sigma)\\ \end{vmatrix} $

Or what about when in orbitals $\Psi_1$ and $\Psi_2$ we have $\varphi_1$ and $\varphi_2$ instead of just $\varphi$? Should I also label $\alpha$=$\alpha_1$ and $\beta=\beta_2$ etc. if $\phi$ has a subscript?

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  • $\begingroup$ You may want to check your indices and notation. Is $\Psi$an orbital or a determinant? $\endgroup$ – my2cts Mar 5 at 16:53

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