Analysis Of Finite Element Scheme For The Time-dependent Schr(?)dinger Equation With Dirichlet Boundary In An Unbounded Strip

This thesis addresses the finite element method for the time-dependent Schr¨odingerequation with Dirichlet boundary condition in an unbounded strip. We first reduce the orig-inal problem into an initial-boundary value problem in a bounded domain by introducinga transparent boundary condition, then fully discretize this reduced problem by applyingCrank-Nicolson scheme in time and bilinear or quadratic finite element approximation inspace. This scheme, by a rigorous analysis,has been proved to be unconditionally stableand convergent, its convergence order has also been obtained. Finally, we give a numericalexample to verify the accuracy of the scheme.