Calculational details

Energy states:

$$ \begin{equation} \vert\Phi_k\rangle = \sum_{i = 0}^{N^L} \sum_{j = 0}^{N^R} C_{ij, k}\vert \varphi^L_i \varphi^R_j\rangle, \tag{18} \end{equation} $$

(Hartree basis)