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Biographical Memoirs Volume 76 (1999) / Chapter Skim
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Valentine Bargmann
Pages 36-49

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From page 37...
... Our question pertainec! to a mathematical fine point clearing with quantum mechanical HamiTtonians expressed as clifferential operators, en c!
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From page 38...
... War II, Bargmann worker! on shock wave studies with John von Neumann en c!
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From page 39...
... a minor industry in the research on such issues. His paper clearing with distinct potentials that exhibit iclentical scattering phase shifts reclirectec!
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From page 40...
... applications of Hilbert space representations by holomorphic functions now commonly known as Bargmann spaces (or sometimes as Segal-Bargmann spaces in view of an essentially parallel analysis of the main features by Irving Segal)
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From page 41...
... that this form of the commutation relation may be represented by the ex
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From page 42...
... Bargmann clefinec! a Hilbert space F of holomorphic functions f~zJ restrictec!
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From page 43...
... All separable en c! infinite-climensional Hilbert spaces are isomorphic.
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From page 44...
... Bargmann realized, however, that the action of tempered distributions on test functions did indeed possess a genuine integral representation in terms of holomorphic functions. For that purpose let 00 u(Z)
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From page 45...
... _00 _00 n=0 Thus, the holomorphic function representation enclowoc! with the Bargmann inner product provides an explicit integral representation for the action of an arbitrary temperer!
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From page 46...
... 99:576-82. 1937 Uber die durch Elektronenstrahlen in Kristallen angeregte Lichtemission.
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From page 47...
... 23:177-99. On a Hilbert space of analytic functions and an associated integral transform.
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From page 48...
... Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, Jahrgang 124, Heft 1, pp.39-44. Zurich: Druck und Verlag Orell Fussli Graphische Betriebe AG.
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Key Terms

  • phase shifts
  • von neumann
  • hilbert space
  • scattering phase
  • holomorphic function

  • mathematical physics
  • analytic functions
  • irreclucible representations
  • central field
  • quantum mechanical

  • wave equations
  • associated integral
  • relativistic wave
  • quantum mechanics
  • function spaces

  • integral transform
  • bargmann inner
  • vierteljahrsschrift der
  • offers expert
  • integral representation

  • feature entirely
  • panel report
  • mark naimark
  • kristallen angeregte
  • theoretical discussion

  • bargmann publisher
  • bargmann analyzed
  • sorely clisappointeci
  • symmetric tensor
  • penetrating simplicity


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