Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Publications of the ...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Publications of the Research Institute for Mathematical Sciences
Article
Data sources: UnpayWall
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article
Data sources: zbMATH Open
Publications of the Research Institute for Mathematical Sciences
Article . 1968 . Peer-reviewed
Data sources: Crossref
Publications of the Research Institute for Mathematical Sciences
Article
Data sources: Microsoft Academic Graph
 View all 2 versions
Claim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Eigenfunction Expansions Associated with the Schrödinger Operator with a Complex Potential and the Scattering Theory

Eigenfunction expansions associated with the Schrödinger operator with a complex potential and the scattering theory
descriptionPublicationkeyboard_double_arrow_right Article 31 Aug 1968Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Publications of the Research Institute for Mathematical Sciences, volume 4, pages 419-466 (issn: 0034-5318, eissn: 1663-4926, Copyright policy )
Authors: Kiyoshi Mochizuki;

doi: 10.2977/prims/1195194884

Eigenfunction Expansions Associated with the Schrödinger Operator with a Complex Potential and the Scattering Theory

Abstract

The main purpose of the paper is to give a generalization of the eigenfunction expansion and scattering theory developed by \textit{A. Ya. Povzner} [Mat. Sb., N. Ser. 32(74), 109--156 (1953; Zbl 0050.32201], \textit{L. D. Faddeev} [Uniqueness of solution of the inverse scattering problem. (Russian). Vestn. Leningr. Univ. 11, No. 7, Ser. Mat. Mekh. Astron. No. 2, 126--130 (1956)] and \textit{T. Ikebe} [Arch. Ration. Mech. Anal. 5, 1--34 (1960; Zbl 0145.36902)] for the selfadjoint Schrödinger operator in \(E_3\) to the non-selfadjoint case. The results are obtained in general under a typical limiting condition on the potential. The last sections contain a discussion of the time-dependent scattering theory and of the uniqueness of the solution for the scattering inverse problem.

Related Organizations
Keywords

Schrödinger operator, Schrödinger equation, Scattering theory for PDEs, quantum theory, Nonselfadjoint operator theory in quantum theory including creation and destruction operators

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 21
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
21
Average
Top 10%
Average
bronze