Laboratory of Computational and Structural Physical Chemistry, Chemistry Department, West University of Timişoara, Pestalozzi Street No.16, Timişoara, RO-300115, Romania; E-Mail:
Int J Mol Sci. 2010 Oct 22;11(10):4124-39. doi: 10.3390/ijms11104124.
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∈[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.
在量子力学的路径积分费曼表述中，从量子涨落对坐标和动量估计的影响方面分析了基本的海森堡测不准关系（HUR）。在对波粒量子信息进行量化时，通过引入特定的粒子和波表示及其比值，以一种紧密的分析方式恢复了基本的 HUR，适用于可观测量子波动哥本哈根二象性的大范围，尽管主要表现为波，同时记录了其与量子涨落的因子 1-n2 的渐进变化，对于精确波粒等效性周围的自由量子演化。讨论了当前粒子到波的比率以及自由演化量子图像对于实验实现、对称破缺和电子局域函数的实际意义。
