Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schrödinger Equation
We present a way to efficiently treat the well-known transparent boundary conditions for the Schrödinger equation. Our approach is based on two ideas: firstly, to derive a discrete transparent boundary condition (DTBC) based on the Crank-Nicolson finite difference scheme for the governing equation. And, secondly, to approximate the discrete convolution kernel of DTBC by sum-of-exponentials for a rapid recursive calculation of the convolution. We illustrate the efficiency of the proposed method on several examples.
A much more detailed version of this article can be found in Arnold et al. .
KeywordsTransformation Rule Fast Calculation Discretization Error Convolution Kernel Absorb Boundary Condition
Unable to display preview. Download preview PDF.
- A. Arnold. Numerically absorbing boundary conditions for quantum evolution equations. VLSI Design, 6:313–319, 1998.Google Scholar