Calculate the generalization of (G_{0}^{ pm}left(vec{r}, vec{r}^{prime} ight)) on the complex plane for energy, (G_{0}left(z ; vec{r},

Calculate the generalization of \(G_{0}^{ \pm}\left(\vec{r}, \vec{r}^{\prime}\right)\) on the complex plane for energy, \(G_{0}\left(z ; \vec{r}, \vec{r}^{\prime}\right)\).