title: Radiation boundary conditions for the numerical solution of the three-dimensional time-dependent Schrödinger equation with a localized interaction.
abstract: Exact radiation boundary conditions on the surface of a sphere are presented for the single-particle time-dependent Schrödinger equation with a localized interaction. With these boundary conditions, numerical computations of spatially unbounded outgoing wave solutions can be restricted to the finite volume of a sphere. The boundary conditions are expressed in terms of the free-particle Green's function for the outside region. The Green's function is analytically calculated by an expansion in spherical harmonics and by the method of Laplace transformation. For each harmonic number a discrete boundary condition between the function values at adjacent radial grid points is obtained. The numerical method is applied to quantum tunneling through a spherically symmetric potential barrier with different angular-momentum quantum numbers l . Calculations for l=0 are compared to exact theoretical results.
authors.affiliation: Soft Condensed Matter, Research Centre Jülich, Institute of Solid State Research, 52425 Jülich, Germany. m.heinen@fz-juelich.de
authors.forename: M
authors.initials: M
authors.lastname: Heinen
authors.forename: H-J
authors.initials: HJ
authors.lastname: Kull