title: Two-dimensional oscillator in time-dependent fields: comparison of some exact and approximate calculations.
abstract: Operator-difference multilayer schemes for solving the time-dependent Schrödinger equation up to sixth order of accuracy in the time step are presented. Reduced schemes for solving a set of coupled time-dependent Schrödinger equations with respect to the hyper-radial variable are devised using expansion of a wave packet over the set of appropriate basis angular functions. Further discretization of the resulting problem is realized by means of the finite-element method. The convergence of the expansion with respect to the number of basis functions and the efficiency of the numerical schemes are demonstrated in the exactly solvable model of an electric-field-driven two-dimensional oscillator (or a charged particle in a constant uniform magnetic field), in which we explicitly observed an effect of the periodical focusing and defocusing of the probability density flux.
authors.affiliation: Joint Institute for Nuclear Research, Dubna, Russia.
authors.forename: O
authors.initials: O
authors.lastname: Chuluunbaatar
authors.forename: A A
authors.initials: AA
authors.lastname: Gusev
authors.forename: S I
authors.initials: SI
authors.lastname: Vinitsky
authors.forename: V L
authors.initials: VL
authors.lastname: Derbov
authors.forename: A
authors.initials: A
authors.lastname: Galtbayar
authors.forename: T
authors.initials: T
authors.lastname: Zhanlav