View in EDS

An application of bilinear integration to quantum scattering.

Saved in:
Bibliographic Details
Title: An application of bilinear integration to quantum scattering.
Authors: García-Raffi, L.M.1 lmgarcia@mat.upv.es, Jefferies, B.2 b.jefferies@unsw.edu.au
Source: Journal of Mathematical Analysis & Applications. Jul2014, Vol. 415 Issue 1, p394-421. 28p.
Subjects: Quantum scattering, Lebesgue integral, Bilinear forms, Selfadjoint operators, Continuous spectrum (Atomic spectrum), Topology, Integral functions
Abstract: Abstract: Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature. [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 94864931
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: An application of bilinear integration to quantum scattering.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22García-Raffi%2C+L%2EM%2E%22">García-Raffi, L.M.</searchLink><relatesTo>1</relatesTo><i> lmgarcia@mat.upv.es</i><br /><searchLink fieldCode="AR" term="%22Jefferies%2C+B%2E%22">Jefferies, B.</searchLink><relatesTo>2</relatesTo><i> b.jefferies@unsw.edu.au</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jul2014, Vol. 415 Issue 1, p394-421. 28p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Quantum+scattering%22">Quantum scattering</searchLink><br /><searchLink fieldCode="DE" term="%22Lebesgue+integral%22">Lebesgue integral</searchLink><br /><searchLink fieldCode="DE" term="%22Bilinear+forms%22">Bilinear forms</searchLink><br /><searchLink fieldCode="DE" term="%22Selfadjoint+operators%22">Selfadjoint operators</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+spectrum+%28Atomic+spectrum%29%22">Continuous spectrum (Atomic spectrum)</searchLink><br /><searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+functions%22">Integral functions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Abstract: Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=94864931
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jmaa.2014.01.055
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 28
        StartPage: 394
    Subjects:
      – SubjectFull: Quantum scattering
        Type: general
      – SubjectFull: Lebesgue integral
        Type: general
      – SubjectFull: Bilinear forms
        Type: general
      – SubjectFull: Selfadjoint operators
        Type: general
      – SubjectFull: Continuous spectrum (Atomic spectrum)
        Type: general
      – SubjectFull: Topology
        Type: general
      – SubjectFull: Integral functions
        Type: general
    Titles:
      – TitleFull: An application of bilinear integration to quantum scattering.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: García-Raffi, L.M.
      – PersonEntity:
          Name:
            NameFull: Jefferies, B.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 07
              Text: Jul2014
              Type: published
              Y: 2014
          Identifiers:
            – Type: issn-print
              Value: 0022247X
          Numbering:
            – Type: volume
              Value: 415
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Journal of Mathematical Analysis & Applications
              Type: main
ResultId 1