正统量子力学的双动态基础 正统量子力学的双动态基础
Diana Taschetto1, Ricardo Correa da Silva2
1Freudental Institute, Department of Mathematics, Faculty of Science, Utrecht University, The Netherlands.
Studies in history and philosophy of science
|December 29, 2024
概括
这项研究揭示了量子力学中矩阵和波力学的等价性需要一个双动函数. 这一发现纠正了关于正规交换关系 (CCR) 起源的误解.
科学领域:
- 物理学的基础 物理学的基础
- 量子力学 形式主义 形式主义 量子力学
- 数学物理 数学物理
背景情况:
- 正统的量子力学依赖于矩阵和波力学的等价性.
- 讨论了正规交换关系 (CCR) 的起源和必要性.
- 之前对施罗丁格波方程和矩阵/波力学等效的分析已经存在.
研究的目的:
- 为了全面研究正统量子力学的动态基础.
- 从矩阵力学中推断出正规的交换关系 (CCR).
- 为了澄清量子力学的历史和数学基础形式主义.
主要方法:
- 对矩阵力学和施罗丁格波形方程的数学分析.
- 对量子力学的发展进行历史检查.
- 对动态基础和行动功能进行哲学研究.
主要成果:
- 从矩阵力学中推断正规的交换关系 (CCR).
- 证明CCR必然从施罗丁格的第一波方程导出.
- 证明矩阵和波力学的等价性是由于双动函数所必需的,而·诺伊曼的过程1和过程2则是从中得到的.
结论:
- 正统的量子力学表现出一种"特殊的双重动力学",这是由于矩阵和波力学假设的等价性.
- 这种双重动态源于假设一种特殊的双重作用功能.
- 这项研究强调了一个基本原则,即物理理论的动态必须源于它的作用功能.
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