The Resource Determining Spectra in Quantum Theory, by Michael Demuth, M. Krishna, (electronic resource)

Determining Spectra in Quantum Theory, by Michael Demuth, M. Krishna, (electronic resource)

Label
Determining Spectra in Quantum Theory
Title
Determining Spectra in Quantum Theory
Statement of responsibility
by Michael Demuth, M. Krishna
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di?erent journals. We collected them, added some and gave some overview that can serve as a platform for further research activities. Spectral theory of Schr ̈ odinger type operators has a long history; however the most widely used methods were limited in number. For any selfadjoint operatorA on a separable Hilbert space the spectrum is identi?ed by looking atthetotalspectralmeasureassociatedwithit;oftenstudyingsuchameasure meant looking at some transform of the measure. The transforms were of the form f,?(A)f which is expressible, by the spectral theorem, as ?(x)dμ (x) for some ?nite measureμ . The two most widely used functions? were the sx ?1 exponential function?(x)=e and the inverse function?(x)=(x?z) . These functions are “usable” in the sense that they can be manipulated with respect to addition of operators, which is what one considers most often in the spectral theory of Schr ̈ odinger type operators. Starting with this basic structure we look at the transforms of measures from which we can recover the measures and their components in Chapter 1. In Chapter 2 we repeat the standard spectral theory of selfadjoint op- ators. The spectral theorem is given also in the Hahn–Hellinger form. Both Chapter 1 and Chapter 2 also serve to introduce a series of de?nitions and notations, as they prepare the background which is necessary for the criteria in Chapter 3
Member of
http://library.link/vocab/creatorName
Demuth, Michael
Dewey number
  • 515.7222
  • 515/.7222
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • xS6k89E1BwY
  • yIqMBvSFHPA
Language note
English
LC call number
QA404.7-405
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Krishna, M.
Series statement
Progress in Mathematical Physics,
Series volume
44
http://library.link/vocab/subjectName
  • Potential theory (Mathematics)
  • Mathematical physics
  • Quantum theory
  • Differential equations, partial
  • Operator theory
  • Functional analysis
  • Potential Theory
  • Mathematical Methods in Physics
  • Quantum Physics
  • Partial Differential Equations
  • Operator Theory
  • Functional Analysis
Label
Determining Spectra in Quantum Theory, by Michael Demuth, M. Krishna, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Measures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (226 p.)
Form of item
online
Isbn
9781280619373
Media category
computer
Media type code
  • c
Other control number
10.1007/0-8176-4439-3
Specific material designation
remote
System control number
  • (CKB)1000000000282770
  • (EBL)303102
  • (OCoLC)222315597
  • (SSID)ssj0000137615
  • (PQKBManifestationID)11157577
  • (PQKBTitleCode)TC0000137615
  • (PQKBWorkID)10088000
  • (PQKB)11551582
  • (DE-He213)978-0-8176-4439-0
  • (MiAaPQ)EBC303102
  • (EXLCZ)991000000000282770
Label
Determining Spectra in Quantum Theory, by Michael Demuth, M. Krishna, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Measures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (226 p.)
Form of item
online
Isbn
9781280619373
Media category
computer
Media type code
  • c
Other control number
10.1007/0-8176-4439-3
Specific material designation
remote
System control number
  • (CKB)1000000000282770
  • (EBL)303102
  • (OCoLC)222315597
  • (SSID)ssj0000137615
  • (PQKBManifestationID)11157577
  • (PQKBTitleCode)TC0000137615
  • (PQKBWorkID)10088000
  • (PQKB)11551582
  • (DE-He213)978-0-8176-4439-0
  • (MiAaPQ)EBC303102
  • (EXLCZ)991000000000282770

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