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math.NA2024
Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory
Matthias Ehrhardt, Chunxiong Zheng
We propose a novel approach to simulate the solution of the time-dependent Schrödinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Wey…
math.NA2020★ 5 cited
Finite Element Approximation of Transmission Eigenvalues for Anisotropic Media
Bo Gong, Jiguang Sun, Tiara Turner +1
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is pos…
math.NA2012★ 80 cited
A time-splitting spectral scheme for the Maxwell-Dirac system
Zhongyi Huang, Shi Jin, Peter Markowich +2
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the…