相空间中扩散过程的量子化渐近性
Quantization as Asymptotics of Diffusion Processes in the Phase Space
摘要：
这项工作是论文arXiv：0803.2669v1[math-ph]的扩展版本，其中公布了主要结果。考虑相空间上波函数的经典扩散过程。结果表明，在$10^{-11}$ { \it sec}阶时，该过程收敛于一个由量子力学考虑并由薛定谔方程描述的过程.该模型研究了与量子力学波函数相对应的相空间中的概率分布。我们利用氢原子光谱移动的Lamb-Retherford实验数据和对扩散过程热原因的假设，估计了模型的参数。在该文件中，它表明，量子力学描述的过程可以出现作为一个近似的描述更精确的模型。对于本文所考虑的模型，当Hamilton函数在坐标、动量和时间的偏差下缓慢变化时，就会出现这种近似，时间间隔的长度是由普朗克常量和扩散强度决定的。
英文摘要：
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of order $10^{-11}$ {\it sec} this process converges to a process considered by quantum mechanics and described by the Schrodinger equation. This model studies the probability distributions in the phase space corresponding to the wave functions of quantum mechanics. We estimate the parameters of the model using the Lamb--Retherford experimental data on shift in the spectrum of hydrogen atom and the assumption on the heat reason of the considered diffusion process. In the paper it is shown that the quantum mechanical description of the processes can arise as an approximate description of more exact models. For the model considered in this paper, this approximation arises when the Hamilton function changes slowly under deviations of coordinates, momenta, and time on intervals whose length is of order determined by the Planck constant and by the diffusion intensities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
