### Abstract

Of the two main objectives we pursue in this paper, the first one consists in the studying operators of the form (∂t−i△Γ)α, α=1/2,−1/2,−1,…, where △_{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. The stability and uniqueness of the solution is investigated for each of these novel boundary conditions.

Original language | English |
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Article number | 011509 |

Number of pages | 23 |

Journal | Journal of Mathematical Physics |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 |

### Keywords

- Operator theory
- Optical scattering
- Schroedinger equations
- Fourier analysis
- Integral transforms

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## Cite this

*Journal of Mathematical Physics*,

*60*(1), [011509]. https://doi.org/10.1063/1.5030875