On the nonreflecting boundary operators for the general two dimensional Schrödinger equation

Vishal Vaibhav

doi:10.1063/1.5030875

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arXiv · 1502.04519

On the nonreflecting boundary operators for the general two dimensional Schrödinger equation

Vishal Vaibhav

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Abstract

Of the two main objectives we pursue in this paper, the first one consists in the studying operators of the form $(\partial_t-i\triangle_Γ)^α,\,\,α=1/2,-1/2,-1,\ldots,$ where $\triangle_Γ$ is the Laplace-Beltrami operator. These operators arise in the context of nonreflecting boundary conditions in the pseudo-differential approach for the general Schrödinger equation. The definition of such operators is discussed in various settings and a formulation in terms of fractional operators is provided. The second objective consists in deriving corner conditions for a rectangular domain in order to make such domains amenable to the pseudo-differential approach. Stability and uniqueness of the solution is investigated for each of these novel boundary conditions.

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Vishal Vaibhav. 2018-12-16. On the nonreflecting boundary operators for the general two dimensional Schrödinger equation. https://doi.org/10.1063/1.5030875

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