Suppose that the probability of finding some particle 1 at \(x_{1}\) is a Gaussian around \(x_{1}\), with standard deviation \(\sigma_{1}\), and the probability of finding another particle 2 at \(x_{2}\) is a Gaussian around \(x_{2}\) with standard deviation \(\sigma_{2}\). What is the condition on the wave functions of the two particles such that the probability to find either particle at the position mentioned is the sum of the two Gaussians?