@ManasDogra From $E = \mathbf{p}^2 + m^2$ we have $E = \pm \varepsilon$ for $\varepsilon = \sqrt{\mathbf{p}^2+m^2}$, therefore the eigenfunctions $e^{i xp}$ of KG are $e^{i( \mathbf{p} \cdot \mathbf{r} - \varepsilon t)}$ and $e^{i( \mathbf{p} \cdot \mathbf{r} + \varepsilon t)}$, so the general solution is a linear combination of such solutions
$$\psi(x,t) = \sum_{\mathbf{p}} N_{\mathbf{p}}[ a_{\mathbf{p}}^{(+)} e^{i( \mathbf{p} \cdot \mathbf{r} - \varepsilon t)} + a_{\mathbf{p}}^{(-)} e^{i( \mathbf{p} \cdot \mathbf{r} + \varepsilon t)}]$$