# Slater determinants: how to calculate?

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?

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