Fast and stable evaluation of the exact absorbing boundary condition for the semi-discrete linear Schrödinger equation in unbounded domains

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region. Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range, particularly involving ultra-low energy. In this work, a new transparent boundary condition (TBC) is proposed for the time-dependent wave packet method. It in principle is of spectral accuracy when typical discrete variable representations are applied. The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function, in contrast with the complex absorbing potential. Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well, which supports resonances states.

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High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation

Yan

Zhao

et al. 2019

International Journal of Computer Mathematics

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Fast and stable evaluation of the exact absorbing boundary condition for the semi-discrete linear Schrödinger equation in unbounded domains

Cited by 3 publications

References 16 publications

A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions

A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions

High-accurate transparent boundary conditions for time-dependent quantum wave packet method

High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation

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