The boundary conditions (BCs) in quantum mechanical scattering are examined in the context of scattering in nanoscale systems, together with the derivative BCs within a finite domain. We introduce the idea of absorbing regions, or stealth regions, that convert the Cauchy BCs into Dirichlet BCs. The action integral for scattering is directly discretized within the framework of the finite element method (FEM) to obtain numerical results using stealth finite elements. In 1D, we demonstrate the method, and then in 2D confined waveguide geometries, we obtain results that go beyond the traditional perturbative or approximate calculations by obtaining the waveguide transmission coefficients. The explicit form of the scattered wavefunction for complex scattering shapes are also obtained.
Worcester Polytechnic Institute
Major Qualifying Project
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