Radiation boundary conditions for the numerical solution of the three-dimensional time-dependent Schroedinger equation with a localized interaction
- Soft Condensed Matter, Research Centre Juelich, Institute of Solid State Research, 52425 Juelich (Germany)
Exact radiation boundary conditions on the surface of a sphere are presented for the single-particle time-dependent Schroedinger 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.
- OSTI ID:
- 21294129
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 79, Issue 5; Other Information: DOI: 10.1103/PhysRevE.79.056709; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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