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范洪义. 量子论中狄拉克符号积分的意义[J]. 物理, 2020, 49(11): 725-735. DOI: 10.7693/wl20201101
引用本文: 范洪义. 量子论中狄拉克符号积分的意义[J]. 物理, 2020, 49(11): 725-735. DOI: 10.7693/wl20201101
FAN Hong-Yi. The physical meaning of the integration of Dirac's symbols[J]. PHYSICS, 2020, 49(11): 725-735. DOI: 10.7693/wl20201101
Citation: FAN Hong-Yi. The physical meaning of the integration of Dirac's symbols[J]. PHYSICS, 2020, 49(11): 725-735. DOI: 10.7693/wl20201101

量子论中狄拉克符号积分的意义

The physical meaning of the integration of Dirac's symbols

  • 摘要: 量子的引入最先是普朗克在1900年为理论“凑合”黑体辐射实验曲线的无奈之举(曲线拟合),然此举如招幡令旗,呼风唤雨,聚溪成流,乘奔御风,浩浩汤汤,终成今日量子流行的漫山遍野之势,是几个能人的集灵思积广益而相辅相成,还是时势造英雄,还是两者兼而有之!普朗克以能量分离的观点看待微观世界,是他在理论推导拟合实验结果逐渐形成的信仰。物理学家狄拉克指出,伟大的物理学家如牛顿和爱因斯坦是靠基本信仰“从上到下”推导出一些大自然的定律的。狄拉克自己的信仰是相信方程的美有时比实验结果更重要,因为实验会有误差。量子的时髦,自然引来众说纷纭,惟在量子园地里“种过树”的人才可能有较深刻的体会。
    作者历经50多年的理论探索,首创了有序算符内的积分理论,对发展量子力学数理基础——狄拉克的符号法略有建树,既能抑制爱因斯坦认为量子力学数学不够完美的抱怨,为爱因斯坦的量子纠缠思想提供纠缠态表象,也从数学上将量子力学几率假说落实到有序算符的正态分布,从而推陈出新、别开生面地丰富量子力学、量子统计力学和量子光学的内容。

     

    Abstract: The introduction of the quantum was led by Planck's reluctant move in 1900 to "guesstimate" the theory to match the experimental curve of blackbody radiation (curve fitting). This move then quickly became a flag summoning a storm. Many streams gathered into a river, riding on the wind and moving forward with great force, eventually resulting in the prevailing popularity of quantum mechanics today. It was the collective wisdom of a few revolutionary people who complemented each other, or it was the times that create heroes, or it was both. Planck's discrete energy view of the world was gradually formed when he derived the theory to fit experimental results. Dirac pointed out that the great physicists, such as Newton and Einstein, deduced their laws of nature from a "top- down" approach based on their fundamental beliefs. Dirac's own belief was that in some cases the beauty of equations is more important than experimental results, because experiments may involve measurement errors.
    The fashion of all things quantum has naturally attracted different opinions, but only those who have actually "planted trees" in the quantum orchard may have a true understanding. After more than 50 years of theoretical exploration, the author's contributions to the development of quantum mechanics, in particular his theory of the integration of Dirac's symbols within an ordered product of operators, has not only developed the mathematics of quantum mechanics, providing Einstein with a representation of the entangled state, but has also incorporated the probability hypothesis of quantum mechanics into the ordered operators' normal distribution, a form of statistical distribution. The present paper should be helpful for quantum experimentalists and theorists to enrich their conceptions, and should also be suitable for all those interested in quantum optics and quantum statistics.

     

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