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Int. J. Mol. Sci. 2010, 11(10), 4124-4139; doi:10.3390/ijms11104124
Article

On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality

1,2
Received: 11 August 2010; in revised form: 27 September 2010 / Accepted: 17 October 2010 / Published: 22 October 2010
(This article belongs to the Special Issue Advances in Molecular Electronic Structure Calculations)
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Abstract: Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor √1-n2, in terms of magnitude n ε [0,1] of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function.
Keywords: quantum fluctuation; Feynman centroid; de Broglie wave-packet; dispersion relationships; quantum duality quantum fluctuation; Feynman centroid; de Broglie wave-packet; dispersion relationships; quantum duality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Putz, M.V. On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality. Int. J. Mol. Sci. 2010, 11, 4124-4139.

AMA Style

Putz MV. On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality. International Journal of Molecular Sciences. 2010; 11(10):4124-4139.

Chicago/Turabian Style

Putz, Mihai V. 2010. "On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality." Int. J. Mol. Sci. 11, no. 10: 4124-4139.


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