Transparent boundary conditions for the stationary Schrödinger equation via Weyl–Titchmarsh theory<sup>*</sup>
Volodymyr Derkach, Carsten Trunk, Jambul Yusupov, D. U. Matrasulov
Abstract
Abstract We propose a general approach for deriving transparent boundary conditions (TBCs) for the stationary Schrödinger equation with arbitrary potential. It is proven that the TBCs can be written in terms of the Weyl–Titchmarsh coefficients. As examples for the application of the proposed approach, two special cases for the stationary Schrödinger equation with the harmonic potential and the Pöschl–Teller potential are considered.
Topics & Concepts
Boundary (topology)Mathematical physicsMathematicsPhysicsMathematical analysisTopological Materials and PhenomenaSpectral Theory in Mathematical PhysicsElectromagnetic Simulation and Numerical Methods