论文标题
连续函数的随机矢量表示及其在量子力学中的应用
Random Vector Representation of Continuous Functions and Its Applica-tions in Quantum Mechanics
论文作者
论文摘要
在本文中揭示了连续函数与随机向量之间的关系，主要含义被描述为对于任何给定的连续函数，必须有一系列概率空间和一系列随机向量的顺序，在这些概率空间之一上，每个随机向量都定义在这些概率空间之一上，从而形成了随机数学预期的顺序，由随机的数学预期由随机的数学预期形成。这是连续函数的随机向量表示，这被认为是在真实函数理论和概率理论之间建立的桥梁。通过这个结论，可以得出有关功能近似理论的有趣结果。连续函数的随机矢量表示在物理学中具有重要的应用。根据结论，如果可以通过连续函数和随机现象来描述大量确定性现象，也可以通过随机变量或向量来描述，那么任何确定性现象都必须是随机现象序列的极限状态。然后，在从随机向量到连续函数的近似值中，我们适当地选择了基本函数，推导了量子力学的重要结论：经典的力学和量子力学是统一的。特别是，引入一个有趣且非常重要的结论是因为宏观对象的质量点运动具有一种波形特征曲线，这称为波质点二元性。
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors where every random vector is defined on one of these probability spaces, such that the sequence of conditional mathematical expectations formed by the random vectors uniformly converges to the continuous function. This is random vector representation of continuous functions, which is regarded as a bridge to be set up between real function theory and probability theory. By means of this conclusion, an interesting result about function approximation theory can be got. The random vectors representation of continuous functionsis is of important applications in physics. Based on the conclusion, if a large proportion of certainty phenomena can be described by continuous functions and random phenomenon can also be described by random variables or vectors, then any certainty phenomenon must be the limit state of a sequence of random phenomena. And then, in the approximation from a sequence of random vectors to a continuous function, the base functions are appropriately selected by us, an important conclusion for quantum mechanics is deduced: classical mechanics and quantum mechanics are unified. Particularly, an interesting and very important conclusion is introduced as the fact that the mass point motion of a macroscopical object possesses a kind of wave characteristic curve, which is called wave-mass-point duality.
