General solution theory for Schrödinger's equation in arbitrary 2D- periodic spatial structures. II: The synthesis of global solutions by layer composition
type: Item
instance of: scholarly article
title: General solution theory for Schrödinger's equation in arbitrary 2D- periodic spatial structures. II: The synthesis of global solutions by layer composition
zbMATH Open document ID: 0653.35020
DOI: 10.1016/0003-4916(88)90152-2
author: Gerhard Wachutka
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: [For part I see the preceding review.] After the first step in the assembly of boundary controlled monolayers method, namely the monolayer boundary value problem, was dealt with in a preceding article, here the synthesis of the original 2D-periodic spatial structure by means of the ``layer composition process'' is investigated. Since the convergence properties of this process are most appropriately discussed in terms of generalized Block waves, these are first analyzed in full detail; special interest is here paid to a ``current sum rule,'' which proves to be fundamental for characterizing the asymptotic behavior of the reflection and transmission operators of the synthesized structure. As an illustrating example, it is finally shown how to calculate global solutions to Schrödinger's equation for a semi- infinite crystal structure (with real physical surface) which match the correct asymptotic boundary data in both the vacuum region and the interior of the crystal deeply in the bulk.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4065498
zbMATH Keywords: boundary controlled monolayers method
zbMATH Keywords: layer composition process
zbMATH Keywords: Block waves
zbMATH Keywords: current sum rule
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: reflection
zbMATH Keywords: transmission
zbMATH Keywords: global solutions
zbMATH Keywords: Schrödinger's equation
zbMATH Keywords: semi-infinite crystal structure
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90152-2
OpenAlex ID: W1974879147
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description: scientific article; zbMATH DE number 4065498