Measurements and Amplitudes

  • Stanley Gudder
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


We present a framework for quantum mechanics based on the concepts of measurements and amplitudes. The measurements are represented by functions and therefore commute. The interference effects characteristic of quantum mechanics are caused by the fact that probabilities are computed using am-plitude functions. Moreover, in order to consider inexact measurements we define fuzzy (or nonsharp) amplitudes. We also study measurements that satisfy a positivity condition and that axe covariant relative to a symmetry group. It is shown that the framework includes stochastic quantum mechanics which in turn includes traditional Hilbert space quantum mechanics.


Hilbert Space Stochastic Quantum Amplitude Density Additive Probability Measure Classical Statistical Theory 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Beltrametti G. Cassinelli, The Logic of Quantum Mechanics, Addison-Wesley Reding 1981.zbMATHGoogle Scholar
  2. 2.
    R. Feynman Space-time approach to non-relativistic quantum mechanics Rev. Mod. Phys. 20 367 398 1948CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    R. Feynman and A. Hibbs Quantum Mechanics and Path Integrals McGraw-Hill New York 1965zbMATHGoogle Scholar
  4. 4.
    S. Gudder Stochastic Methods in Quantum Mechanics North Holland New York 1979.Google Scholar
  5. 5.
    S. Gudder, “A theory of amplitudes”, (to appear).Google Scholar
  6. 6.
    S. Gudder, “Fuzzy amplitude densities and stochastic quantum mechanics”, Found. Phys. (to appear).Google Scholar
  7. 7.
    J. Jauch Foundations of Quantum Mechanics Addison-Weley Reding 1968zbMATHGoogle Scholar
  8. 8.
    G. Mackey Mathematical Foundations of Quantum Mechanics Benjamin New York 1963zbMATHGoogle Scholar
  9. 9.
    C. Piron Foundations of Quantum Mechanics Benjamin New York 1976Google Scholar
  10. 10.
    E. Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime Reidel Dordrecht 1984zbMATHGoogle Scholar
  11. 11.
    L. Schulman Techniques and Aplications of Path Integration Wiley (Inter- science) New York 1981Google Scholar
  12. 12.
    V. Varadarajan Geometry of Quantum Theory vol. I Van Nostrand Princeton 1968zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Stanley Gudder
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenverUSA

Personalised recommendations