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Discrete Transparent Boundary Conditions for Schrödinger-Type Equations

✍ Scribed by Frank Schmidt; David Yevick

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
445 KB
Volume
134
Category
Article
ISSN
0021-9991

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✦ Synopsis

We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schro ¨dinger-type solution of (1) only in a finite subdomain of ⍀ in order to equations. Our method supplies boundary conditions for theexamine the time evolution in the surrounding of a specifamily of implicit one-step discretizations of Schro ¨dinger's equation fied object. In our 1D-case, we accordingly separate the in time. The use of Mikusin ´ski's operator approach in time avoids infinite domain ⍀ into three slab-like parts: an interior direct and inverse transforms between time and frequency domains

and thus implements the boundary conditions in a direct manner. ᮊ 1997 Academic Press t Ͼ 0͖ containing the physically relevant part of the solution and two neighboring slabs of infinite thickness ⍀ l ϭ ͕x, t ʦ R ͉ x Յ x l , t Ͼ 0͖ and ⍀ r ϭ ͕x, t ʦ R ͉ x Ն x r , t Ͼ 96

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