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Implementing exact absorbing boundary condition for the linear one-dimensional Schrödinger problem with variable potential by Titchmarsh--Weyl theory
- Publication Year :
- 2009
- Publisher :
- Weierstrass Institute, 2009.
-
Abstract
- A new approach for simulating the solution of the time-dependent Schrödinger equation with a general variable potential will be proposed. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a rational function with respect to a suitable spectral parameter. With the proposed method we can overcome the usual high-frequency restriction for absorbing boundary conditions of general variable potential problems. We end up with a fast computational algorithm for absorbing boundary conditions that are accurate for the full frequency band.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....77026b54372ccaa69c8f62be960750ed
- Full Text :
- https://doi.org/10.20347/wias.preprint.1426