of several carriers in the same QD, we numerically solve the time-independent Schrödinger equation, $\hat{H}\Psi=E\cdot\Psi$, via exact diagonalization. The index $\textbf{n}$ is the set of quantum numbers required to describe all particles. The Hamiltonian, $\hat{H}$, of the system is: $$\label{eq:H}
\hat{H}=\sum_{i=1}^N\left[\frac{-\hbar^2}{2m_i^*}\Delta_i + V\left(\vec{x}\right)\right] + \hat{C}.$$ $\hat{C}$ is the Coulomb operator, which is given by: $$\label{Eq:CoulombOp}
 \hat{C}=\frac{1}{4\pi\epsilon_0\epsilon_r}\sum_{i,\ j,\ i\neq j}^N\frac{c_i\cdot c_j}{\abs{r_i-r_j}}.$$ The term $c_i=\pm e$ is the charge of a particle (electron or hole). As we are considering fermionic particles, the overall wavefunction is antisymmetric under particle exchange. Therefore, we consider $\hat{H}$ in a basis of antisymmetrized Slater determinants: $$\Psi_{\textbf{n}}=\hat{\mathcal{A}}\prod_{i=1}^N\phi_{n_i}\left(x_i,\ \sigma_i\right).$$ These Slater determinants are constructed from the single-particle solutions, $\phi_{n_i}\left(x_i,\ \sigma_i\right)$, of Eq. \[eq:H\]. The asymmetrization operator, $\hat{\mathcal{A}}$, constructs a Slater-determinant, which is asymmetric under the exchange of identical particles. To express $\hat{H}$ in the basis $\{\Psi_{\textbf{n}}\}$, the matrix elements $\bra{\Psi_{\textbf{n}}}{\hat{H}}\ket{\Psi_{\textbf{m}}}$ have to be computed. The Slater-Condon rules [@Slater1929; @Condon1930] transform these multi-particle matrix elements into two-particle Coulomb matrix elements. The Slater-Condon rules for the two-particle Coulomb operator, $\hat{C}$, are: $$\begin{aligned}
\label{Eq:SlCondon}
&\bra{\Psi_{\textbf{n}}}{\hat{H}}\ket{\Psi_{\textbf{n}}} = \frac{1}{2}\sum_{i,\ j,\ i\neq j}^N\left[V_{ijij} - V_{ijji}\right]\\
&\bra{\Psi_{\textbf{n}}}{\hat{H}}\ket{\Psi_{\textbf{n}\left(h,k\right)}} = \sum_{i=1}^N\left[V_{hiki}- V_{hiik}\right]\\
&\bra{\Psi_{\textbf{n}}}{\hat{H}}\ket{\Psi_{\textbf{n}\left(h,k,l,m\right)}} = V_{hlkm} - V_{hlmk}.\end{aligned}$$ The index $\textbf{n}\left(h,k\right)$ indicates that this wavefunction has been obtained by 