title: Numerical solutions of the time-dependent Schrödinger equation in two dimensions.
abstract: The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrödinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite-difference scheme in space. Extra care has to be taken for the needed precision of the time development. The method permits a systematic study of the accuracy and efficiency in terms of powers of the spatial and temporal step sizes. To illustrate its utility the method is applied to several two-dimensional systems.
authors.affiliation: Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada.|Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
authors.forename: Wytse
authors.initials: W
authors.lastname: van Dijk
authors.affiliation: Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada.
authors.forename: Trevor
authors.initials: T
authors.lastname: Vanderwoerd
authors.affiliation: Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada.
authors.forename: Sjirk-Jan
authors.initials: SJ
authors.lastname: Prins