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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
Footnote:
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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.