Weak Convergence of Finite Element Approximations of Stochastic Linear Schr\"{o}dinger equation driven by additive Wiener noise

A standard finite element method discretizes the stochastic linear Schr"{o}dinger equation driven by additive noise in the spatial variables. The weak convergence of the resulting approximate solution is analyzed, and it is established that the weak convergence rate is twice that of the strong convergence.