Analysis Of Finite Element Method For One-dimensional Time-dependent Schr(?)dinger Equation On Unbounded Domain

In this thesis, we propose a fully discrete scheme by using the artificial boundary technique for one-dimensional time-dependent Schrodinger equation on unbounded domain, and give its theoretical analysis. First, we reduce the original problem into an initial-boundary value problem in a bounded domain by introducing an artificial boundary condition, and then fully discrete this problem by applying Grank-Nicolson scheme in time and linear or quadratic finite element approximation in space. By a rigorous analysis, this scheme has been proved to be unconditionally stable and convergent, and its convergence order has also been obtained.