Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme
Maike Schulte - Institut für Angewandte und Numerische Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster, Germany (email)
Abstract: We consider the two-dimensional time-dependent Schrödinger equation with the new compact nine-point scheme in space and the Crank-Nicolson difference scheme in time. For the resulting difference equation we derive discrete transparent boundary conditions in order to get highly accurate solutions for open boundary problems. Numerical experiments illustrate the perfect absorption of outgoing wave independently of their impact angle at the boundary. Finally, we apply inhomogeneous discrete transparent boundary conditions to the transient simulation of quantum waveguides.
Keywords: Schrödinger equation, transparent boundary conditions, finite difference
schemes, compact discretization schemes.
Received: September 2007; Revised: October 2007; Available Online: February 2008.
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