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On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality
Laboratory of Computational and Structural Physical Chemistry, Chemistry Department, West University of Timişoara, Pestalozzi Street No.16, Timişoara, RO-300115, Romania
Theoretical Physics Institute, Free University Berlin, Arnimallee 14, 14195 Berlin, Germany
Received: 11 August 2010; in revised form: 27 September 2010 / Accepted: 17 October 2010 / Published: 22 October 2010
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
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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.
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.
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.