# Probability of superposition of states

hi could someone please verify that my calculated probability for superposition of states is correct (i derived it myself from a simpler equation) where $\Psi=c1\psi1 e^{-iE1t}+c2\psi2 e^{-iE2t}$ and $\psi_i, c_i \in \mathbb{R}$

$|\Psi|^2=(c_1\psi_1)^2+(c_2\psi_2)^2+2Re[c_1c_2\psi_1\psi_2e^{i(E2-E1)t}]$

thanks!