Skip to main content

First elements of a theory of quantum mechanical limit distributions

  • 456 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 928)

Keywords

  • Positive Definite Function
  • Convolution Theorem
  • Fundamental Lemma
  • Canonical Pair
  • Positive Definite Kernel

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. BARGMANN, On Unitary Ray Representations of Continuous Groups. Annals Math. 59, 1–46 (1954).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. C.D. CUSHEN, R.L. HUDSON, A Quantum Mechanical Central Limit Theorem. J. Appl. Prob. 8, 454–469 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. CZKWIANTIANC, Symmetric Semistable Measures on Rn and Symmetric Semistable Distribution Operators in Quantum Mechanics. Reports Math. Physics 17, 89–99 (1980).

    CrossRef  Google Scholar 

  4. J. DIXMIER, Sur la relation i (PQ-QP)=1. Compositio Math. 13, 263–270 (1958).

    MathSciNet  MATH  Google Scholar 

  5. T. DRISCH, A Generalisation of Gleason’s Theorem. Int. J. Theor. Physics 18, 239–243 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. T. DRISCH, Die Sätze von Bochner und Lévy für Gleason-Maße. Arch. Math. 34, 60–68 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. T. DRISCH, Zur Realisierung unabhängiger kanonischer Paare. Arch. Math. 34, 357–370 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. A. GLEASON, Measures on the Closed Subspaces of a Hilbert Space. J. Math. Mech. 6, 885–893 (1957).

    MathSciNet  MATH  Google Scholar 

  9. G.W. MACKEY, Unitary Representations of Group Extensions I. Acta Math. 99, 265–311 (1958).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. G.W. MACKEY, Unitary Group Representations in Physics, Probability and Number Theory. Benjamin, Reading (Mass.) 1978.

    MATH  Google Scholar 

  11. J. v. NEUMANN, Die Eindeutgkeit der Schrödingerschen Operatoren. Math. Ann. 104, 570–578 (1931).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. K.R. PARTHASARATHY, Multipliers on Locally Compact Groups. Springer Lecture Notes Math. 93, Heidelberg 1969.

    Google Scholar 

  13. K.R. PARTHASARATHY, K. SCHMIDT, Positive Definite Kernels, Continuous Tensor Products and Central Limit Theorems. Springer Lecture Notes Math. 272, Heidelberg 1975.

    Google Scholar 

  14. B. SIMON, Topics in Functional Analysis. In: R. STREATER, Mathematics of Contemporary Physics, London—New York 1972.

    Google Scholar 

  15. K. URBANIK, Stable Symmetric Probability Laws in Quantum Mechanics. In: Springer Lecture Notes 472, Heidelberg 1975.

    Google Scholar 

  16. V.S. VARADARAJAN, Probability in Physics and a Theorem on Simultaneous Observability. Comm. Pure App. Math. 15, 189–217 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. V.S. VARADARAJAN, Geometry of Quantum Theory I, II. Van Nostrand, Princeton 1968.

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Drisch, T. (1982). First elements of a theory of quantum mechanical limit distributions. In: Heyer, H. (eds) Probability Measures on Groups. Lecture Notes in Mathematics, vol 928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093218

Download citation

  • DOI: https://doi.org/10.1007/BFb0093218

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11501-4

  • Online ISBN: 978-3-540-39206-4

  • eBook Packages: Springer Book Archive