Quantum Mechanics from a Heisenberg-Type Equality

  1. Dr. Dietrich Papenfuß3,
  2. Professor Dr. Dieter Lüst4 and
  3. Professor Dr. Wolfgang P. Schleich5
  1. Michael J. W. Hall1 and
  2. Marcel Reginatto2

Published Online: 29 NOV 2007

DOI: 10.1002/9783527610853.ch30

100 Years Werner Heisenberg: Works and Impact

100 Years Werner Heisenberg: Works and Impact

How to Cite

Hall, M. J. W. and Reginatto, M. (2002) Quantum Mechanics from a Heisenberg-Type Equality, in 100 Years Werner Heisenberg: Works and Impact (eds D. Papenfuß, D. Lüst and W. P. Schleich), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610853.ch30

Editor Information

  1. 3

    Alexander von Humboldt-Stiftung, Bonn, Germany

  2. 4

    Humboldt Universität, Institut für Physik, Germany

  3. 5

    Universität Ulm, Abteilung f. Quantenphysik, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Author Information

  1. 1

    Theoretical Physics, RSPSE, Australian National University, Canberra ACT 0200 Australia

  2. 2

    Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany

Publication History

  1. Published Online: 29 NOV 2007
  2. Published Print: 27 AUG 2002

ISBN Information

Print ISBN: 9783527403929

Online ISBN: 9783527610853

SEARCH

Keywords:

  • quantum physics;
  • quantum mechanics from a Heisenberg-type equality;
  • Heisenberg Suncertainty relation;
  • replaced;
  • exact equality for suitably chosen measures of position and momentum uncertainty;
  • exact uncertainty relation;
  • moving from classical mechanics to quantum mechanics;
  • Schrödinger equation

Summary

The usual Heisenberg uncertainty relation, ΔX ΔP ≥ h̄/2, may be replaced by an exact equality for suitably chosen measures of position and momentum uncertainty, which is valid for all wave functions. This exact uncertainty relation, δX ΔPnc ≡ h̄/2, can be generalised to other pairs of conjugate observables such as photon number and phase, and is sufficiently strong to provide the basis for moving from classical mechanics to quantum mechanics. In particular, the assumption of a nonclassical momentum fluctuation, having a strength, which scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrödinger equation.