• Media type: E-Article
  • Title: Radiation boundary conditions for the numerical solution of the three-dimensional time-dependent Schrödinger equation with a localized interaction
  • Contributor: Heinen, M. [Author]; Kull, H.-J. [Author]
  • imprint: APS, 2009
  • Published in: Physical review / E 79, 056709 (2009). doi:10.1103/PhysRevE.79.056709
  • Language: English
  • DOI: https://doi.org/10.1103/PhysRevE.79.056709
  • ISSN: 1539-3755
  • Keywords: Laplace transforms ; Schrodinger equation ; angular momentum ; quantum theory ; Green's function methods
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  • Description: Exact radiation boundary conditions on the surface of a sphere are presented for the single-particle time-dependent Schrodinger 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.
  • Access State: Open Access