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

International Journal of Molecular Sciences

关键词: quantum fluctuation;    Feynman centroid;    de Broglie wave-packet;    dispersion relationships;    quantum duality;   

DOI  :  10.3390/ijms11104124

来源: mdpi

【 摘 要 】

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 , in terms of magnitude n∈[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.

【 授权许可】

CC BY   
© 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.