Formula_11171

\[\begin{gathered}\mathscr{H}=\int d^{3} \boldsymbol{r}\left[\sum_{\alpha} \Psi_{\alpha}^{+}(\boldsymbol{r}) \mathscr{H}_{e}(\boldsymbol{r}) \Psi_{\alpha}(\boldsymbol{r})+\right. \\+U(\boldsymbol{r}) \Psi_{\alpha}^{+}(\boldsymbol{r}) \Psi_{\alpha}(\boldsymbol{r})+\Delta(\boldsymbol{r}) \Psi_{1 / 2}^{+}(\boldsymbol{r}) \Psi_{-1 / 2}^{+}(\boldsymbol{r})+ \\\left.+\Delta^{*}(\boldsymbol{r}) \Psi_{-1 / 2}(\boldsymbol{r}) \Psi_{1 / 2}(\boldsymbol{r})\right],\end{gathered}\]