Nonlinear filtering and time varying Schrodinger equation

Based on our previous work we have successfully reduced the nonlinear filtering problem for Yau filtering system to the timevarying Schrodinger equation. In order to solve the nonlinear filtering problem, one needs to solve the time-varying Schrodinger equation with an arbitrary initial condition. We then solve the time-varying Schrodinger equation by constructing the fundamental solution explicitly via a system of nonlinear ODES in case the potential is quadratic in state variables. This system of nonlinear ODES is solved explicitly by the power series method.